Question

Find the matrix A' for T relative to the basis B'. T: R2 + R2, T(x, y) = (3x - y, 4x), B' = {(-2, 1), (-1, 1)} A' =

Answer 1

Given:
and  

T(2, y) = (5.r - y, 4.1)

B' = {(-2,1),(-1,1)}

Let,

→ 5.r - y = (-2) + (-1)02: 4.c = c + c

C2 = 4.0 - (-9.2 + y)

C2 13.C - Y

Hence,

T(2, y) = (-9.r + y) (-2,1) + (13.1 - y) (-1,1)

$\Rightarrow T(-2,1)=(-9\times (-2)+1)(-2,1)+ (13\times (-2)-1)(-1,1)$

      

197-2.11-27(-1.1)

and

$={\color{Blue} 10}(-2,1){\color{Blue} -14}(-1,1)$

which is the required matrix A' for T relative to the basis B'

Due to HOMEWORKLIB POLICY we are required to do just the first question please ask the second question separately.

Hope this helps!