Question Type 1: Performing simple linear operations on matrices Exercises

Simplify $3A + 2B - A$ for $A = \begin{pmatrix}2 & 1\\0 & 3\end{pmatrix},\quad B = \begin{pmatrix}-1 & 4\\5 & 2\end{pmatrix}.$

Compute $3E - F$ for $E = \begin{pmatrix}1 & -1 & 2\\0 & 3 & -2\\4 & 1 & 0\end{pmatrix},\quad F = \begin{pmatrix}2 & 0 & -1\\3 & -1 & 1\\0 & 2 & 4\end{pmatrix}.$

If $X + 2A = 3B$ and $A = \begin{pmatrix}1 & 0\\-1 & 2\end{pmatrix},\quad B = \begin{pmatrix}2 & 3\\1 & 0\end{pmatrix},$ find $X$.

Evaluate $5\begin{pmatrix}0 & -3\\2 & 1\end{pmatrix} - 3\begin{pmatrix}1 & 2\\0 & 4\end{pmatrix}.$

Calculate $4\begin{pmatrix}2 & 1\\3 & 5\end{pmatrix} + 2\begin{pmatrix}1 & 0\\-1 & 2\end{pmatrix}.$

Given $A = \begin{pmatrix}1 & -2\\3 & 4\end{pmatrix},\quad B = \begin{pmatrix}2 & 0\\-1 & 5\end{pmatrix},$ find $2A + 3B$.

Verify the distributive property $k(A+B)=kA+kB$ by computing both sides for $k=2,\quad A=\begin{pmatrix}1 & 2\\3 & -1\end{pmatrix},\quad B=\begin{pmatrix}0 & 4\\-2 & 5\end{pmatrix}.$

Compute $3A$ where

Let $C = \begin{pmatrix} -1 & 2 & 0 \\ 3 & 1 & -2 \end{pmatrix}, \quad D = \begin{pmatrix} 2 & -3 & 4 \\ 0 & 5 & -1 \end{pmatrix}.$

Compute $C - 2D$.

Calculate $-3C + 4D$.

Simplify $2(A+B) - (A - B)$ where $A = \begin{pmatrix}1 & 2\\3 & 0\end{pmatrix},\quad B = \begin{pmatrix}0 & -1\\4 & 5\end{pmatrix}.$

Compute $-2B$ where $B = \begin{pmatrix}1 & 3\\-2 & 4\end{pmatrix}.$