Help with Linear Algebra

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Help with Linear Algebra

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1. Suppose that $T$ is the matrix transformation defined by the matrix $A$ and $S$ the matrix transformation defined by $B$ where

$$ A=\left[\begin{array}{rrr} 3 & -1 & 0 \\ 1 & 2 & 2 \\ -1 & 3 & 2 \end{array}\right], \quad B=\left[\begin{array}{rrr} 1 & -1 & 0 \\ 2 & 1 & 2 \end{array}\right] $$

a. If $T: \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}$, what are the values of $m$ and $n ?$ What values of $m$ and $n$ are appropriate for the transformation $S ?$

b. Evaluate the matrix transformation $T\left(\left[\begin{array}{r}1 \\ -3 \\ 2\end{array}\right]\right)$.

c. Evaluate the matrix transformation $S\left(\left[\begin{array}{r}-2 \\ 2 \\ 1\end{array}\right]\right)$.

d. Evaluate the matrix transformation $S \circ T\left(\left[\begin{array}{r}1 \\ -3 \\ 2\end{array}\right]\right)$.

e. Find the matrix $C$ that defines the matrix transformation $S \circ T$.

Linear-Algebra

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A 2016-] Lt 3 2 R² R² Then T: R3 43 and S Time - RM Then n=3 and m=3 of The dimension domain of s co-domain af I must be equ

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