Question: Let T:R^3-->R^2 be a linear transformation such that: (a) Find a matrix A such that T(x) = Ax. (b) Is T onto? Is it one-to-one?

Let T:R^3-->R^2 be a linear transformation such that:

(a) Find a matrix A such that T(x) = Ax. (b) Is T onto? Is it one-to-one? (c) Find all vectors v such that T(v) = (d) Is there a linear transformation S : R2 -> R3 such that So T : R3 -> R3 is one-to-one? Explain why or why not. (Remember, So T(x) = S(T(x)). )

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Question 21 , 22 , 24 , 25. Question 21 Let TA be the linear operator corresponding to multiplication by the matrix A, that is, TA (x) = Ax. Which of the following are True? O T (el) = e1, where Th =...

Q?4: Let T:R^3?R^2 be a linear transformation such that T([?(1@0@0)])=[?(1@-2)], T([?(0@1@0)])=[?(-2@4)] and T([?(0@0@1..3@-6)]. [8 marks] Find a formula for T(X),X?R^3. [4 marks] Find a matrix A...

linear algebra question Let us consider the linear transformation T : RS -> RS defined as follows: T(x) is obtained from x = ($1, 12, 13) by . first rotating the vector of its first two components...

NO CREDIT WILL BE GIVEN FOR USING METHODS OUTSIDE OF CHAPTER 1. 7. Verify (B - C)A = BA - CA. (10 points) 1. The following represents the reduced row echelon form of an augmented matrix obtained from...

Let T be a linear transformation from R2 to R2 defined by T(x, y) = (2x - y, x + y). a) Find the matrix of T with respect to the bases B = {(1, 1), (2,1)} and B = {(-1,2), (1,1)}. (4 marks) (4 marks)...

3 Systems of differential equations In Sections 3.8-3.10 we will reduce the problern of finding all solutions of (1) to the much simpler algebraic problern of solving simultaneous linear equations of...

E. (4 pts) Let x=[x1x2],v1=[26], and v2=[13], and let T:R2R2 be a linear transformation that maps x onto x1v1+x2v2. Find a matrix A such that T(x) is Ax for all x. F. (4 pts) Assume T:R3R2 is a...

3 Systems of differential equations 7. Suppose that AD =DA for all matrices A. Prove that D is a multiple of the identity matrix. 8. Prove that AxadjA=detAxl. In each of Problems 9-14, find the...

MUST SHOW STEP BY STEP WORK!! 1. Choose h and k such that the system has (a) no solution and (b) many solutions. Give separate answers for each part. X1 + hx2 = 2 3x1 + 9x2 = 3k 2. Determine if b is...

Name: Math 308 J, Winter 2017 Proof HW #2 Due 2/6/17 Proof Homework 2 WARNING: Aside from 3c.), REFERRING TO THE MATRICES OF LINEAR MAPS WILL NOT HELP YOU. It will just make your proof harder than it...

Let hy6t denote the three-month holding yield (in percent) from buying a six-month T-bill at time (t - 1) and selling it at time t (three months hence) as a three month T-bill. Let hy3t-1 be the...

How do you find the median for a data set: a. With an odd number of values? b. With an even number of values?

If the returns of two assets are perfectly positively correlated, an investor who puts half of their savings into each will have a higher expected return. reduce risk but lower the expected return....

On 1 March 2007 DB Limited issued R560 000 15% debentures at R98. The debentures were to be redeemed at par in four equal annual payments starting 28 February 2010. Required: Journalise the above...