Question

25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R – RM is defined by Tv) = Av, where A is as follows. 0 1 -6 1 -1 7 40 0 1 9 1 (a) Find T(0, 3, 2, 1). STEP 1: Use the definition of T to write a matrix equation for TO, 3, 2, 1). T10, 3, 2, 1) = and STEP 2: Use your result from Step 1 to solve for T(0, 3, 2, 1). Ti0, 3, 2, 1) = 1 100 (b) Find the preimage of (0, 0, 0). STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation. 0 1 -6 1 Tw, x, y, z) = -1 7 40 0 1 9 1 y 0 Lett be any real number. Set z = t and solve for w, x, and y in terms of t. W = z = STEP 2: Use your result from Step 1 to find the preimage of (0, 0, 0). (Enter each vector as a comma-separated list of its components.) The preimage is given by the set of vectors {( ): t is any real number). Need Help? Read it Talk to a Tutor Submit Answer 26. [0/1 Points) DETAILS PREVIOUS ANSWERS LARLINALG8 6.2.001. Find the kernel of the linear transformation. (If all real numbers are solutions, enter REALS.) T; R = R2, Tx, y) = (0, 0) ker(7) = { (xy) :X, Y CRY YER} X Need Help? Read it Watch It Talk to a Tutor

Answer 1

( 25i Given that T: 1R RM such that 7(u) = Au -61 A: -17 40 0 co @ T (0,3,2,1)= 761741-33978france 3 T (0,3,2,1) © 29 22 © for preimage of (0,0,0). 6 o 17 2 4 0 191 T (W ,ky, 2) 16-17 Neew, 0 1-61 R R3-R, 0 -6 i -1 7 4 0 0 191 -P ๆ 0 0 15 0 0 |-6 -61 -1 7 4 0 0 0 15 O 77 100

4 169 го x - by+2=0 2 A - The x= 64-2/ -W + 7x + 4y = 0 -W+7(-2) +0=0 w = -72 take , 2=t, we get x=-t, W-7t.y=0 preinage of (0,0,0) = {674,-4,0,t): teid} 6 Given that T.R² 112² such that T(1,41 = (0,0) Ker(t)= {(x,y) {(29): = {(x,y) : xy EAR} {(x,y): ay are real numbers} . : T (key)=6,03} +(779) E122) Ans =