Question

Let A be the matrix below and define a transformation T:ℝ3→ℝ3 by T(U) = AU. For each of the vectors B below, find a vector U such that T maps U to B, if possible. Otherwise state that there is no such U. A = 2−6−42−6−1−394a) B = 2614−31< Select an answer >b) B = −816< Select an answer >

Question 8 [10 points] R by T(U) = AU. For each of the vectors B below, find a vector U such that I maps Let A be the matrix below and define a transformation T: R U to B, if possible. Otherwise state that there is no such U. 2 -6 -4 A= 2 -6 -1 | -3 9 4 < Select an answer > a) B= 1-31 -8) b) B= | 1 < Select an answer >

Answer 1

TOT Answes= a) → <8,,-43 - 6)<s,l,3> TU)= AU - B E Range space ------ a sebution i e. 2 - 6 -4 126 1-87 2 -6 -7 / 14 9 4 7-31 / Te we are doing both the parts I simultaneously. R2 7R2-R1 ~ R3 R3 + 3 R 12 co -6 0 -4 3 -12 2 R₂ R3 R₃ R3 RI R l i o -u / 3 Lo 0 -4 / +3 * Az = -4 , b3=3 . & a-3a2 + 8 = 13 0 - 3 b2-6=-4 - a=5+3a2 a = b = 2+3 b2 let a=1 a, = 8 let b2 = 1 b1=5 Az = -40 63= 3 .. (5, 1,3 Lo T+8) [267 [57 7- 7 /7 14tik Zu I [-31) So for B answer is (8,1,-4) & for part B) & Answer Spiral J 6 7