Prove the following statement. Your work should be legible, and all your logic should be clear and justified. Let S and T be invertible linear transformations from R" to R". If T (S(x)) = x for all xã € R", then S(T(x)) = ☎ for all ☎ ¤ Rª.

Q: A 20ft by 28ft swimming pool is filled with water. The depth is measured at regular intervals,…

A: Given: A swimming pool 20 ft by 28 ft filled with water and depth is measured at regular interval…

Q: Find the value of k for which the matrix has rank 2. k = 1 A = -8-7 2 -1 -3 -4 k

A: The given matrix is A=-8-7-62-1-41-3k. For what value of k rank of A is 2.

Q: Given: Differential equation: y" - 2y' = sin x To find: The solution of given D.E. using Power…

A: Given: Differential equation: y'''-2y'=sin xTo find: The solution of given D.E. using Power series.

Q: Evaluate the limit 1 - cos(t); t + (t + 2)j + (t + 2)²k) lim t-0 Enter your answer in i, j, k form.

A: Here we have to find limit in the vector form.

Q: 11. Graph the function ƒ(x) = −2x² + 2x + 4 and its reciprocal on the same or separate axes. Explain…

A: 11. Given that the function is                        f(x)=-2x2+2x+4.

Q: © 2013 by HK BOLIDE Naked Eye Observation: The chart above shows how you can identify the source of…

A: The given flow chart is: We have to (i) write the steps of the flow chart that lead to unknown…

Q: The principal P is borrowed at a simple interest rate r for a period P = $5000, r = 5.5%, t = 6…

A: The principal P is borrowed at a simple interest rate r for a period of time t. We need to find the…

Q: Consider the curve in the xy-plane defined by c(t) = (²² – 5,81² – 13t). At what point (x, y) does…

A:

Q: Find the Riemann sum approximation of the double integral -150 •16 (3x (3x - 9y) dA where D is the…

A:

Q: Draw a continuous function f (x) with all of the following properties: f(0) = 0, f(1) = 1, f' (0) =…

A:

Q: The graph to the right shows the heart rate of a person watching a short romantic film, where x…

A: Answer: From the given graph, Highest peaks in the graph= maximum heart rate  By looking at the…

Q: Find the number of distinguishable arrangements of the letters of the word. QUINTILLION There are…

A:

Q: 10 A- 6+ 18 13 5(7) -+5(9)²

A: Matlab code to write above expression on matlab is

Q: A tank initially contains 50 gal of pure water. A solution containing 2 lb/gal of salt is pumped…

A:

Q: Find a linearization at a suitably chosen integer near a at which the given function and its d are…

A:

Q: Give parametric equations that describe a full circle of radius R, centered at the origin with…

A: To Find : Parametric equation of a circle of radius R centered at the origin, where t parameter…

Q: A car traveling directly N60°E covered 500 miles between noon and 10 pm. If its starting point is…

A: Given Data: Let us consider the given data, Distance =500 miles. Time =10 hour. To Find : x and y.

Q: Consider lines ₁ and ₂. l₁ : [x, y] = [1, 4] + t[−7, 2] l₂: [x, y] = [-2, 6] + t[k, 9] a) For what…

A:

Q: The Solid Trust Savings & Loan Company has set aside $25 million for loans to home buyers. Its…

A: Sol:- Let's start by defining some variables: Let x be the amount allocated for luxury…

Q: The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's…

A:

Q: 1 3 uz (0, t) = uz (π, t) = 0, ux Ux 10x U t = - U x x u(x, 0) = ㅠ 0 Σχ Σπ

A: The given problem is to find the solution for the given heat equation partial differential equation…

Q: Use the following simplex tableau. xy S1 S2 7 0 0 59 -3 1 0 130 -8 0 1 71 $1 S₁ = (a) State the…

A:

Q: John discovered that he also has a pair of boots and a pair of dress shoes in his closet. Make a…

A:

Q: Consider the initial value problem for function y given by, where u(t - c) denotes the step function…

A:

Q: Let ƒ : [0, 1] → R be a continuous function. We let ran(f) = {y | y = f(x) for some x = [0, 1] }.…

A: In this solution we will discuss the image of a continuous function. We know that a function f:A→B…

Q: Evaluate the expression. 11 C3 11 C3=

A:

Q: Find all solutions to the equation [50]114 Y = [8]114 for Y EZ114. Justify your answer.

A:

Q: i) axb=-bxa ii)_a•(b+c)=a•b+a•c iii) (a+b)+c=a+(b+c)

A:

Q: For the function of two variables defined by ƒ(u, v) = u² cos v + v² sin u, select the option that…

A: Given: Let consider the function of two variables, f(u,v)=u2cos v+ v2 sin uWe have to find ∂f∂u…

Q: f(x) = [0,-1<x<0 2,0<x< 1 Compute the coefficients by hand. Then, give the maple code used to plot…

A: To find the Fourier series of a periodic function f(x) with period 2L, we can use the following…

Q: Construct the payoff matrix for this game. (Enter the values as integer percents. So 1% would be…

A:

Q: The x y-coordinate plane is given. The curve with two parts enters the window in the second quadrant…

A: The graph satisfies the conditions, The curve with two parts enters the window in the second…

Q: Write set of odd numbers greaten than 5 and less than 15 using set builder notation.

A:

Q: 2. Use Fundamental Theorem of Calculus to compute (a) Jedz where C:z = eit,0 < t < T; (b) fc zdz for…

A: (b) The given integral is ∫Cz13dz for the principal branch of z13. The curve C is defined as…

Q: Suppose F(x, y, z)=(x, y, 52). Let W be the solid bounded by the paraboloid z = zª + the closed…

A: Given:  F→x, y, z=x, y, 5z Paraboloid z=x2+y2 Plane z=9 To find:  a ∬S F→·dA→ b (i) Flux out of the…

Q: The graph of y=5^x is translated 8units to the right and 3 units downward. What is the transformed…

A: The given function is y=5x. We have to translate function 8 units to the right and 3 units downward.

Q: Describe the region on the unit sphere that is covered by the image of the Gauss map of the…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: 8. Two planes take off at the same time from an airport. The first plane is flying at 255 miles per…

A: If there are no wind currents blowing, we have to find how far apart are they after 2 hours. andWe…

Q: Solve the linear programming problem by the simplex method. Maximize P = 15x + 13y subject to x + y≤…

A:

Q: Find the flux of the vector field  V(x, y, z) = 3xy2i + 3x2yj + z3k out of the unit sphere. Use the…

A: Sol:- The surface integral of a vector field V over a closed surface S is given by: ∬SV.dS=∫∫∫V.n dV…

Q: I also found that the expression was divisible by 13 at n=6 and n=10. Is there anyway you could…

A: Any number n can be written in the form          n = 3m, or 3m+1, or 3m + 2 for some integer m.…

Q: The circle graph shows a breakdown of spending for the average household using 365 days worked as a…

A:

Q: 2. Solve the following system of equations by Gauss Elimination method (without pivoting): iv)…

A:

Q: Solve the following higher-order differential equations: 1. (D56D4 + 8D³ + 6D²9D)y = x + ex

A:

Q: Subset: Let X = { 10,20,20,20, 30, 40, 10 } and Y = { 20, 40 }.  Is Y the subset or proper subset of…

A: Given  X = { 10,20,20,20, 30, 40, 10 } Y = { 20, 40 }  We need to find whether Y is subset or proper…

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞…

A: We will estimate the limit.

Q: An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV…

A: Let X1 = number of TV ads X2 = number of radio ads X3 = number of newspaper ads       We have to…

Q: a. a d g -3b - 3e -3h b c e f h i -a b. -d -g 3c + x b 3f+y e 3i+z h

A:

Q: 8 -3 2 -3 ㅋ - 2 ㅏㅏ -3

A:

Q: Calculate the least square solution to the system of equation Svar: [J]. 4x-3y=-2 2x+3y=1 3x+3y=-2

A: