031 Review Part 2, Problem 7

(a) Let  $T:\mathbb {R} ^{2}\rightarrow \mathbb {R} ^{2}$  be a transformation given by

$T{\bigg (}{\begin{bmatrix}x\\y\end{bmatrix}}{\bigg )}={\begin{bmatrix}1-xy\\x+y\end{bmatrix}}.$

Determine whether  $T$  is a linear transformation. Explain.

(b) Let  $A={\begin{bmatrix}1&-3&0\\-4&1&1\end{bmatrix}}$  and  $B={\begin{bmatrix}2&1\\1&0\\-1&1\end{bmatrix}}.$  Find  $AB,~BA^{T}$  and  $A-B^{T}.$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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