# Find the matrices: a)A + B b) A - B c) -4A d)3A + 2B A=begin{bmatrix}4 & 1 3 & 2 end{bmatrix} ,B=begin{bmatrix}5 & 9 0 & 7 end{bmatrix}

Question
Matrices
Find the matrices:
a)A + B
b) A - B
c) -4A
d)3A + 2B
$$A=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix} ,B=\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}$$

2021-02-01
Step 1: Given:
We have matrices $$A=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix} ,B=\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}$$
We have to answer the following.
Step 2: Calculation
a) A+B
$$\Rightarrow A+B=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix}+\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}=\begin{bmatrix}9 & 10 \\ 3 & 9 \end{bmatrix}$$
b) A-B
$$\Rightarrow A-B=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix}-\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}=\begin{bmatrix} -1 & -8 \\ 3 & -5 \end{bmatrix}$$
c) -4A
$$\Rightarrow -4A=-4 \begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix} = \begin{bmatrix} -16 & -4 \\ -12 & -8 \end{bmatrix}$$
d) 3A+2B
$$\Rightarrow 3A+2B=3\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix}+2\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}=\begin{bmatrix} 12 & 3 \\ 9 & 6 \end{bmatrix} + \begin{bmatrix} 10 & 18 \\ 0 & 14 \end{bmatrix} = \begin{bmatrix} 22 & 21 \\ 9 & 20 \end{bmatrix}$$

### Relevant Questions

Find the following matrices: a) A + B.
(b) A - B.
(c) -4A.
(d) 3A + 2B.
$$A=\begin{bmatrix}6 & 2 & -3 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 3 \end{bmatrix}$$
Find the matrices:
a)A + B
b) A - B
c) -4A
d)3A + 2B.
$$A=\begin{bmatrix}3&1 &1\\-1&2&5 \end{bmatrix} , B=\begin{bmatrix}2&-3 &6\\-3&1&-4 \end{bmatrix}$$
The 2 \times 2 matrices A and B below are related to matrix C by the equation: C=3A-2B. Which of the following is matrix C.
$$A=\begin{bmatrix}3 & 5 \\-2 & 1 \end{bmatrix} B=\begin{bmatrix}-4 & 5 \\2 & 1 \end{bmatrix}$$
$$\begin{bmatrix}-1 & 5 \\2 & 1 \end{bmatrix}$$
$$\begin{bmatrix}-18 & 5 \\10 & 1 \end{bmatrix}$$
$$\begin{bmatrix}18 & -5 \\-10 & -1 \end{bmatrix}$$
$$\begin{bmatrix}1 & -5 \\-2 & -1 \end{bmatrix}$$

Let M be the vector space of $$2 \times 2$$ real-valued matrices.
$$M=\begin{bmatrix}a & b \\c & d \end{bmatrix}$$
and define $$M^{\#}=\begin{bmatrix}d & b \\c & a \end{bmatrix}$$ Characterize the matrices M such that $$M^{\#}=M^{-1}$$

Given:
$$A=[[-2,3],[0,1]]$$
$$B=[[8,1],[5,4]]$$
Find the following matrices:
a. A + B
b. A - B
c. -4A
d. 3A + 2B.
find which of the given matrices are nonsingular.
a) $$\begin{bmatrix}1 & 2 &-3 \\-1 & 2&3 \\ 0 &8&0 \end{bmatrix}$$
b)$$\begin{bmatrix}1 & 2 &-3 \\-1 & 2&3 \\ 0 &1&1 \end{bmatrix}$$
c) $$\begin{bmatrix}1 & 1 &2 \\-1 & 3&4 \\ -5 &7&8 \end{bmatrix}$$
d) $$\begin{bmatrix}1 & 1 &4&-1 \\1 & 2&3&2 \\ -1 &3&2&1\\-2&6&12&-4 \end{bmatrix}$$
Compute the indicated matrices, if possible .
A^2B
let $$A=\begin{bmatrix}1 & 2 \\3 & 5 \end{bmatrix} \text{ and } B=\begin{bmatrix}2 & 0 & -1 \\3 & -3 & 4 \end{bmatrix}$$
Let $$A=\begin{bmatrix}2 & -1&5 \\-3 & 4&0 \end{bmatrix} \text{ and } B=\begin{bmatrix}-3 & -4&2 \\-1 & 0&-5 \end{bmatrix}$$
$$[A]=\begin{bmatrix}3 & 4 & 5 \\1 & 7 & 8 \\ 2 & 6 & 9\end{bmatrix}$$
$$A=\begin{bmatrix}2 & -3&7&-4 \\-11 & 2&6&7 \\6 & 0&2&7 \\5 & 1&5&-8 \end{bmatrix} B=\begin{bmatrix}3 & -1&2 \\0 & 1&4 \\3 & 2&1 \\-1 & 0&8 \end{bmatrix} , C=\begin{bmatrix}1& 0&3 &4&5 \end{bmatrix} , D =\begin{bmatrix}1\\ 3\\-2 \\0 \end{bmatrix}$$