Let T: R3 R3 be defined by T(x,y,z) = (x + y,x - y - z, x +z). (A) Show that T is a matrix transformation by finding its standard matrix. (solution) (B) Find the determinant of the matrix in (A) above. (solution) (C) Show that the matrix in (A) above is invertible without finding its inverse. [Do NOT use your answer in (B) above.] (solution) (D) Find the inverse of the matrix in (A) above
Answers
(A) The standard matrix for T(x, y, z) = (x + y, x - y - z, x + z) is [ 1 1 0; 1 -1 -1; 1 0 1].(B) The determinant of the matrix in (A) is det(T) = 2.(C) The matrix in (A) is invertible because its determinant is non-zero. (D) The inverse of the matrix in (A) is [ 1/2 1/2 1/2; 1/2 -1/2 1/2; -1/2 1/2 1/2].
To find the standard matrix for T(x, y, z) = (x + y, x - y - z, x + z), we apply the transformation to the standard basis vectors of R3 and put the results into a matrix. We have:
T(1, 0, 0) = (1, 1, 1)
T(0, 1, 0) = (1, -1, 0)
T(0, 0, 1) = (0, -1, 1)
So, the standard matrix for T is [ 1 1 0; 1 -1 -1; 1 0 1].
To find the determinant of the matrix in (A), we can either expand along the first row or the second column. We choose to expand along the first row:
det(T) = 1(det[ -1 -1; 0 1]) - 1(det[ 1 -1; 0 1]) + 0(det[ 1 1; -1 -1])
= -1 - (-1) + 0
= 2
Since the determinant of the matrix in (A) is non-zero, the matrix is invertible. This is a consequence of the fact that a square matrix is invertible if and only if its determinant is non-zero.
To find the inverse of the matrix in (A), we use the formula A^-1 = (1/det(A))adj(A), where adj(A) is the adjugate (transpose of the cofactor matrix) of A. We already know that det(T) = 2, so we only need to find adj(T):
adj(T) = [ -1 1 1; -1 -1 2; 0 -1 -1]
Therefore, the inverse of the matrix in (A) is:
T^-1 = (1/2)adj(T) = [ 1/2 1/2 1/2; 1/2 -1/2 1/2; -1/2 1/2 1/2]
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Related Questions
A typical tool used to communicate project status is a: A. Project network diagram. B. Gantt Chart C. A PERT chart. D. Both A and B are correct
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The correct answer is D. Both A and B are correct.
Both a Project Network Diagram and a Gantt Chart are commonly used tools to communicate project status. Each of these tools provides a visual representation of project tasks, their dependencies, and their respective timelines.
A Project Network Diagram, also known as a project schedule network diagram or an activity network diagram, illustrates the sequence and dependencies of project activities. It uses nodes (representing activities) and arrows (representing dependencies) to depict the logical flow of tasks in a project.
A Gantt Chart is a horizontal bar chart that shows project tasks as bars along a timeline. It displays the start and end dates of each task, allowing project managers and stakeholders to visualize the overall project schedule and understand the progress of individual tasks.
Both these tools are effective in communicating project status and can be used together or individually, depending on the project's requirements and preferences of the project team.
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Given AVXY and AWWZ, what is the perimeter of the trapezoid WXYZ? Round to the nearest 100th
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Using the triangle proportionality theorem, the perimeter can be determined as: 114.61 units.
What is the Triangle Proportionality Theorem?The triangle proportionality theorem states that if a line segment that is parallel to one side of a triangle, joins the other two sides of the triangle, it divides the two sides proportionally.
Thus, find VW using the triangle proportionality theorem:
VW/WX = VZ/ZY
SubstituteVW/36 = (44 - 27.5)/27.5
VW/36 = 16.5/27.5
VW = 21.6
Find XY using Pythagorean Theorem:
XY = √(VX² - VY²)
XY = √(57.6² - 44²)
XY = 37.17
Find WZ:
WZ/XY = VZ/VY
SubstituteWZ/37.17 = 16.5/44
WZ = 13.94
Perimeter of Trapezoid WXYZ = WX + XY + YZ + WZ
Perimeter = 36 + 37.17 + 27.5 + 13.94
Perimeter = 114.61 units.
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HEY guys I’m back Nooooo I was so happy I didn’t have to use this but Can Someone help me do this I’ll Mark you The Brainliest Pls I need HELPPPPP!
Answers
Answer:
hey cutie
Step-by-step explanation:
Answer:
Language:
1. Circle All terms
2. 12 or 13
3. 8
4. 12 or 13
Plot:
Get a graph for this one, the number is the first parameter is x, find that x value along the x axis then after finishing it locate v, find y value along the y axis.
Solve:
1. x = 3
2. x = 1
3. x = 3
4. x = x = 5
5. x = 8
6. x = 12
7. x = 9
8. x = 4
9. x = 3
10. x = 6
11. x = 4
12. x = -12
13. x = 5
14. x = 6
15. x = 16
Step-by-step explanation:
Variables - in algebra is a symbol or a letter.
Constants - are numbers
Coefficients - are the numbers that are with variables
Use this description and circle the examples.
For the plot use a gird, or gets a coordinate plane.
Lastely for the Solve example minus or plus the constant with the coefficient and variable forum the constant outside that has been equal to. Then divide by the variable coefficient, and you will get your x value. Example:
34 - 13 = 21 / 7 thus x = 3
Help me out with this question!! 50 points
Answers
C
The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C
The correct answer is D) The first inequality should be s + h ≤ 1800.
The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.
The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.
(-8)^-n determine either abosulte convergence, conditional convergence or divergence for the series
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The series \(\sum_{n = 1}^{00} (- 1) ^ n * (\sqrt{n ^ 2 + 1} - n)\) converges conditionally.
To determine the convergence of the series \(\sum_{n = 1}^{00} (- 1) ^ n * (\sqrt{n ^ 2 + 1} - n)\), we can analyze its behavior.
First, let's simplify the expression inside the series:
(-1)ⁿ * (√(n² + 1) - n) = (-1)ⁿ * (√(n² + 1) - n) * (√(n² + 1) + n) / (√(n² + 1) + n)
= (-1)ⁿ * (n² + 1 - n²) / (√(n² + 1) + n)
= (-1)ⁿ / (√(n²+ 1) + n)
Now, let's consider the absolute value of the terms in the series:
|(-1)ⁿ / (√(n² + 1) + n)| = 1 / (√(n² + 1) + n)
To determine the convergence or divergence of the series, we can examine the behavior of the terms as n approaches infinity.
As n approaches infinity, the denominator √(n² + 1) + n also approaches infinity. Therefore, the absolute value of the terms in the series approaches zero.
However, the series alternates signs with (-1)ⁿ, which means the series does not converge absolutely. It also does not satisfy the conditions for the Alternating Series Test since the limit of the absolute value of the terms is not monotonically decreasing.
Therefore, the series converges conditionally.
In summary, the series \(\sum_{n = 1}^{00} (- 1) ^ n * (\sqrt{n ^ 2 + 1} - n)\) converges conditionally.
The complete question is:
determine either abosulte convergence, conditional convergence or divergence for the series \(\sum_{n = 1}^{00} (- 1) ^ n * (\sqrt{n ^ 2 + 1} - n)\)
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Find the volume of the cone. Use 3.14 for pi. Round your answer to the nearest tenths
place.
Answers
The volume of the cone is approximately 37.7 cubic units
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
To find the volume of a cone, we use the formula:
V = (1/3) * π * r² * h
where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.
Plugging in the given values, we get:
V = (1/3) * 3.14 * 3² * 4 ≈ 37.7
Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).
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how do you solve this please help
Answers
Answer:
thanks
Step-by-step explanation:
I have been patient trying to get a job
What is the correct numerical expression for "9 times 4 added to the difference of 3 and 2?"
9 x 4 + (3 − 2)
9 x (4 + 3) − 2
9 + (4 x 3) ÷ 2
9 − 2 x 4 + 3
Answers
The correct Numerical expression for "9 times 4 added to the difference of 3 and 2" is 37.
The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:
9 x 4 + (3 − 2)
To solve this expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
Step 1: Evaluate the subtraction inside the parentheses:
3 − 2 = 1
Step 2: Rewrite the expression with the simplified value:
9 x 4 + 1
Step 3: Perform the multiplication:
9 x 4 = 36
Step 4: Add the products:
36 + 1 = 37
Therefore, the correct numerical expression for "9 times 4 added to the difference of 3 and 2" is 37.
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4.7x4.7x4.7 thats about it
Answers
Answer:
103.823
Step-by-step explanation:
It's just 4.7 to the third power, so I multiplied to get 103.823. :)
What is the length of the missing side?
(your answer should be in decimal format up to two decimal place OR left as a square root)
Answers
Answer:
the length of missing side is √115(ie.10.723)
Verify each identity. tan (A-B)=tan A-tan B/1+tan A tan B
Answers
The given identity is verified as follows:
Starting with the left side of the equation: tan(A - B)
Using the trigonometric identity for the difference of two angles, we have:
tan(A - B) = (tan A - tan B) / (1 + tan A tan B)
This matches the right side of the equation: (tan A - tan B) / (1 + tan A tan B)
To verify the given identity, we need to manipulate the left side of the equation using trigonometric identities and simplify it until it matches the right side of the equation.
Starting with the left side, we have tan(A - B). Using the trigonometric identity for the difference of two angles, we can express this as (tan A - tan B) / (1 + tan A tan B).
By applying the identity for the difference of two angles, we can rewrite tan(A - B) as (tan A - tan B) / (1 + tan A tan B). This is because tan(A - B) is equivalent to the ratio of the difference of the tangent values of the angles A and B, divided by 1 plus the product of the tangent values of angles A and B.
After simplification, we see that the left side of the equation matches the right side of the equation, (tan A - tan B) / (1 + tan A tan B).
Therefore, the given identity is verified.
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Can you please explain how I got it wrong and how to get it right (thank you)
Answers
Answer:
x = 42°
Step-by-step explanation:
Since (3x+3) and 129 are corresponding angles, we can set them equal to one another and solve for x.
3x + 3 = 129
- 3 - 3
3x = 126
/3 / 3
x = 42°
Please, Solve for Y
3x - y = -13
(Correct answer gets brainliest)
Answers
Answer:
y = 13 +3x
i answered in the comments, bc it wasnt lettin me actually answer
Step-by-step explanation:
3x - y = - 13
-3x -3x
-y = -13 - 3x
divide everything by -1
y = 13 + 3x
hope this helpsss!!!
mr laub has three children
Answers
Answer:
He does?
Step-by-step explanation:
What type of function is this:
a1 = 2
an = an-1+4
Arithmetic and Explicit
Arithmetic and Recursive
Geometric and Explicit
Geometric and Recursive
Answers
Answer:
Gravity, also called gravitation, in mechanics, the universal force of attraction acting between all matter. ... On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth's mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects.
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Answers
Answer:
what should we have to do here
I don't understand
A popular restaurant advertises that it delivers its orders within 30 minutes. Suppose the average delivery time for one restaurant is 27 minutes with a standard deviation of three minutes. What is the delivery time with a z-score of 1.2?
23.4 minutes
27.4 minutes
28.2 minutes
30.6 minutes
Answers
Answer:
30.6 minutes
Step-by-step explanation:
Using the normal distribution, it is found that the delivery time with a z-score of 1.2 is of 30.6 minutes.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by:
\(\mu = 27, \sigma = 3\).
The delivery time with a z-score of 1.2 is X when Z = 1.2, hence:
\(Z = \frac{X - \mu}{\sigma}\)
\(1.2 = \frac{X - 27}{3}\)
X - 27 = 3 x 1.2
X = 30.6.
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divide 9y power 2 by 3
divide (8x power 2 +4x ) by 2x
Answers
Answer:
1=27
2=34
Step-by-step explanation:
1)9y power 2÷3
or, y=9 power 2÷3
or, y=9×9÷3
or, y=81÷3
or, y=27
2) (8x power 2+4x)÷2
=(8x×8+4x)÷2
=(64x+4x)÷2
=68x÷2
or, x=68÷2
or, x=34
sandwiches are being bought bye us--passive to active
Answers
Give the value of M and C.
Answers
Answer:
y = 5x - 3, so M = 5 and C = -3.
a triangular sail has a base length of 2.5. the area of the sail is 3.75 square meters . how tall is it
Answers
Answer:
The sail is 3 meters tall.
Step-by-step explanation:
3.75 x 2 = 7.5
7.5 / 2.5 = 3
Congruence Statements-
Just the answer for #1 please!
Answers
Answer:
FDE
Step-by-step explanation:
Teresa tiene 12 años , su hermano pere tiene 7 y su padre 44. QUANTOS AÑOS TIENE Q PASAR PARA Q LA SUMA DE LAS EDADES DE TERESA Y SPERE SEAN IGUALES
Answers
Answer:
Tienen que pasar 25 años para que la suma de las edades de Teresa y Pere sean iguales a la edad de su padre.
Step-by-step explanation:
Dado que Teresa tiene 12 años, su hermano Pere tiene 7 y su padre 44, para determinar cuántos años tienen que pasar para que la suma de las edades de Teresa y Pere sean iguales a la edad de su padre se debe realizar el siguiente cálculo:
12 + 7 = 19
44 - 19 = 25
44 + 25 = 69
(12 + 25) + (7 + 25) = 37 + 32 = 69
Por lo tanto, tienen que pasar 25 años para que la suma de las edades de Teresa y Pere sean iguales a la edad de su padre.
3m=5(m+3)-3 How do I solve it
Answers
Simplifying
3m = 5(m + 3) + -3
Reorder the terms:
3m = 5(3 + m) + -3
3m = (3 * 5 + m * 5) + -3
3m = (15 + 5m) + -3
Reorder the terms:
3m = 15 + -3 + 5m
Combine like terms: 15 + -3 = 12
3m = 12 + 5m
Solving
3m = 12 + 5m
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '-5m' to each side of the equation.
3m + -5m = 12 + 5m + -5m
Combine like terms: 3m + -5m = -2m
-2m = 12 + 5m + -5m
Combine like terms: 5m + -5m = 0
-2m = 12 + 0
-2m = 12
Divide each side by '-2'.
m = -6
Simplifying
m = -6
3m=5(m+3)-3 can be solved to get m=-6
An equation is a mathematical statement that shows that two mathematical expressions are equal. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
3m=5(m+3)-3, This can be solved by following the steps mentioned below:
On solving parenthesis
3m=5m+15-3
3m=5m+12
Transposing like terms together,
3m-5m=12
-2m=12
Dividing both sides by -2
-2m/-2=12/-2
m=-6
So, m=-6 for given equation 3m=5(m+3)-3
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In a population of 200 mice brown fur is dominant to gray fur. of 120 of the 200 mice have brown fur, what is the frequenzy?
Answers
The frequency of mice that are heterozygote is 0.3492
It is required to find the frequency.
What is frequency?The number of waves that pass a fixed point in unit time being, measured in hertz(Hz).The number of cycles or vibrations undergone during one unit of time by a body in periodic motion.
Given:
Population =200 mice
Gray fur mice= 120 mice
By the use of Hardy-Weinberg equation we have,
Hardy-Weinberg equation is given by
p² + 2pq + q² = 1 and p + q = 1
where, 2pq is the heterozygote frequency.
p² = 120/200
p = 0.7746
p + q = 1
q = 0.2254
Heterozygote frequency = 2pq = 2(0.2254)(0.7746) = 0.3492
Therefore, the frequency of mice that are heterozygote is 0.3492.
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14x+38(16x+16) . pleaaseee
Answers
14x + 38(16x + 16) = 14x + (38 * 16x) + (38 * 16)
Multiplying 38 by 16x gives 608x, and multiplying 38 by 16 gives 608. So the expression becomes:
14x + 608x + 608
Combining like terms, we get:
622x + 608
Therefore, 14x + 38(16x + 16) simplifies to 622x + 608.
I need this down thanks
Answers
Answer:
c
a
Step-by-step explanation:
Answer:
5. is C which is 9.
6. is B which is 37.
Step-by-step explanation:
The first on is C. 9 because to find the interquartile range you need to subtract the upper quartile range by the lower quartile range. The upper is 16 and the lower is 7 so you do 16-7 which is 9.
The last question is B. 37 because the lower quartile range is first line in the box plot which is 37.
On a mountain, the temperature decreases by 6.5°C for every 1000 metres increase in height.
At 2000 metres the temperature is 10 °C.
Find the temperature at 6000 metres.
Answers
Based on the temperature at 2,000 meters and the rate of temperature change, the temperature at 6,000 meters is -16°C.
The difference between 2,000 meters and 6,000 meters is:
= 6,000 - 2,000
= 4,000 meters
For every 1,000 meters increase, the temperature will drop by 6.5 °C. At 4,000 meters:
= 6.5 x 4,000 / 1,000
= 26 °C
The temperature will reduce by 26°C to become:
= Temperature at 2,000 - Temperature change
= 10 - 26
= -16 °C
In conclusion, the temperature is -16 °C.
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Slabs of meat 0.0635 m thick are to be frozen in an air blast freezer at 244.3 K (-28.9 °C). The meat initially at the freezing temperature of 270.4 K (-2.8 °C). The meat contains 75% moisture. The heat transfer coefficient is h= 142 w/m2K. The physical properties are rho=1057 kg/m3 for the unfrozen meat and k=1.038 W/mK for the frozen meat. Calculate freezing time.
Answers
To calculate the freezing time of the meat slabs, we need to consider the heat transfer coefficient and temperature differences. The freezing process involves heat transfer from the meat to the surrounding air in the freezer, leading to a decrease in temperature.
First, we need to calculate the temperature difference (ΔT) between the meat and the surrounding air. The initial temperature of the meat is 270.4 K (-2.8 °C), and the target temperature is 244.3 K (-28.9 °C). Therefore, ΔT = 244.3 - 270.4 = -26.1 K.
Next, we can calculate the heat transfer rate using the formula:
Q = h * A * ΔT
To calculate the surface area (A) of the meat slabs, we need to know the dimensions. The thickness of the slabs is given as 0.0635 m. However, the length and width of the slabs are not provided in the question.
Once we have the heat transfer rate, we can determine the freezing time by dividing the heat required to freeze the moisture in the meat slabs by the heat transfer rate. The heat required to freeze the moisture can be calculated as:
Q_freezing = (0.75 * weight_of_moisture) * latent_heat_of_freezing
The weight of moisture and the latent heat of freezing values are not provided, so we cannot determine the exact freezing time without this information.
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Find the value of x. PLEASE HELP ILL MARK YOU THE BRAINLIEST!! I've been trying to solve this thing for 30 minutes and I still have nothing
Answers
Answer:
x = 3
Step-by-step explanation:
When two chords intersect inside a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.
4 * 2x = 3 * (x + 5)
8x = 3x + 15
5x = 15
x = 3