# 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}

Question
Matrices
Find the following matrices: a) A + B.
(b) A - B.
(c) -4A.
(d) 3A + 2B.
$$A=\begin{bmatrix}6 & 2 & -3 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 3 \end{bmatrix}$$

2021-02-03
Step 1
Given matrices:$$A=\begin{bmatrix}6 & 2 & -3 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 3 \end{bmatrix}$$
To find:
a) A + B.
(b) A - B.
(c) -4A.
(d) 3A + 2B.
Solution:
$$A=\begin{bmatrix}6 & 2 & -3 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 3 \end{bmatrix}$$
a)$$A+B=\begin{bmatrix}6 & 2 & -3 \end{bmatrix}+\begin{bmatrix}4 & -2 & 3 \end{bmatrix}$$
$$\Rightarrow A+B=\begin{bmatrix}(6+4) & (2-2) & (-3+3) \end{bmatrix}$$
$$\Rightarrow A+B=\begin{bmatrix}10 & 0 & 0 \end{bmatrix}$$
b) $$A-B=\begin{bmatrix}6 & 2 & -3 \end{bmatrix}-\begin{bmatrix}4 & -2 & 3 \end{bmatrix}$$
$$\Rightarrow A-B=\begin{bmatrix}(6-4) & (2-(-2)) & (-3-3) \end{bmatrix}$$
$$\Rightarrow A-B=\begin{bmatrix}2 & 4 & -6 \end{bmatrix}$$
c)$$-4A=-4\begin{bmatrix}6 & 2 & -3 \end{bmatrix}$$
$$\Rightarrow -4A=\begin{bmatrix}-24 & -8 & 12 \end{bmatrix}$$
d)$$3A+2B=3\begin{bmatrix}6 & 2 & -3 \end{bmatrix}+2\begin{bmatrix}4 & -2 & 3 \end{bmatrix}$$
$$\Rightarrow 3A+2B=\begin{bmatrix}18 & 6 & -9 \end{bmatrix}+\begin{bmatrix}8 & -4 & 6 \end{bmatrix}$$
$$\Rightarrow 3A+2B=\begin{bmatrix}(18+8) & (6-4) & (-9+6) \end{bmatrix}$$
$$\Rightarrow 3A+2B=\begin{bmatrix}26 & 2 & -3 \end{bmatrix}$$
Step 2
Result
a)$$A+B=\begin{bmatrix}10 & 0 & 0 \end{bmatrix}$$
b)$$A-B=\begin{bmatrix}2 & 4 & -6 \end{bmatrix}$$
c)$$-4A=\begin{bmatrix}-24 & -8 & 12 \end{bmatrix}$$
d)$$3A+2B=\begin{bmatrix}26 & 2 & -3 \end{bmatrix}$$

### Relevant Questions

Find the matrices:
a)A + B
b) A - B
c) -4A
d)3A + 2B
$$A=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix} ,B=\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}$$
Find the matrices:
a)A + B
b) A - B
c) -4A
d)3A + 2B.
$$A=\begin{bmatrix}3&1 &1\\-1&2&5 \end{bmatrix} , B=\begin{bmatrix}2&-3 &6\\-3&1&-4 \end{bmatrix}$$

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 $$M^{\#}=M^{-1}$$

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.
$$A=\begin{bmatrix}3 & 5 \\-2 & 1 \end{bmatrix} B=\begin{bmatrix}-4 & 5 \\2 & 1 \end{bmatrix}$$
$$\begin{bmatrix}-1 & 5 \\2 & 1 \end{bmatrix}$$
$$\begin{bmatrix}-18 & 5 \\10 & 1 \end{bmatrix}$$
$$\begin{bmatrix}18 & -5 \\-10 & -1 \end{bmatrix}$$
$$\begin{bmatrix}1 & -5 \\-2 & -1 \end{bmatrix}$$
Find the following matrices:
a) A + B.
(b) A - B.
(c) -4A.
$$A=\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix} , B=\begin{bmatrix}6 & 10&-2 \\0 & -12&-4\\-5&2&-2 \end{bmatrix}$$
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.
Refer to the following matrices.
$$A=\begin{bmatrix}2 & -3&7&-4 \\-11 & 2&6&7 \\6 & 0&2&7 \\5 & 1&5&-8 \end{bmatrix} B=\begin{bmatrix}3 & -1&2 \\0 & 1&4 \\3 & 2&1 \\-1 & 0&8 \end{bmatrix} , C=\begin{bmatrix}1& 0&3 &4&5 \end{bmatrix} , D =\begin{bmatrix}1\\ 3\\-2 \\0 \end{bmatrix}$$
Identify the row matrix. Matrix C is a row matrix.
Giventhe following matrices:
$$A=\begin{bmatrix}1 & 2 &9 \\ -1 & 2 &0 \\ 0&0&4 \end{bmatrix} B=\begin{bmatrix}0 & -1 \\ 2 & 6 \end{bmatrix} C=\begin{bmatrix}2 & 1 \\ 0 & 0 \end{bmatrix} D=\begin{bmatrix}1 \\ 2 \\ -4 \end{bmatrix}$$
Identify the following:
a) A-B
b) B+C
c) C-D
d) B-C
$$A=\begin{bmatrix}1& -1&2 \\3&4&5\\0&1&-1 \end{bmatrix} , B=\begin{bmatrix}0&2&1 \\3&0&5\\7&-6&0 \end{bmatrix} \text{ and } C=\begin{bmatrix}0&0&2 \\3&1&0\\0&-2&4 \end{bmatrix}$$
i)2A-B+2C ii)A+B+C iii)4C-2B+3A iv)$$(A \times B)-C$$
Let $$A=\begin{bmatrix}2 & -1&5 \\-3 & 4&0 \end{bmatrix} \text{ and } B=\begin{bmatrix}-3 & -4&2 \\-1 & 0&-5 \end{bmatrix}$$