Question

X1 Let x = V = and v2 - and let T: R2R2 be a linear transformation that maps x into xxv, + XxV2. Find a matrix A such that T(x) is Ax for each x. X2 A=

Answer 1

-8 x = NG 22 = q= -6 27 2 T: RTR T(X) = 4 4 + x rh 8 Then the metrix Correspondand to X is Associated T(!)- 2 Mi) = V2 -7 G - co vi 8 A 1 -7 -6 2) TIR? R² be a linear toonform T4)=(1,3) (1,0) + 31011) Tl₂)= (-4,6) = -411,0) + 61011) 8,-2)= 3(1,0) -210,1) Then Tes) [A] = []

w T: R² R be lineas transformat T(4,8) (26+22 32 +222) TW) = (5,78) ( 2+2 , 37,+233) 5=xtų Els 18= 34+242 (ii) را فو - ) 8 = 22 4 = 4 o] Then T (18) 18