# For Exercise , perform the indicated operations if possible. A=begin{bmatrix}4 & 1&-3 2 & 4 &6end{bmatrix} , B=begin{bmatrix}1 & 9 0 & -13&5 end{bmatrix} , C=begin{bmatrix}0 & 1&-4 2 & -1 &8end{bmatrix} A+B=?

Question
Matrices
For Exercise , perform the indicated operations if possible.
$$A=\begin{bmatrix}4 & 1&-3 \\2 & 4 &6\end{bmatrix} , B=\begin{bmatrix}1 & 9 \\0 & -1\\3&5 \end{bmatrix} , C=\begin{bmatrix}0 & 1&-4 \\2 & -1 &8\end{bmatrix}$$
A+B=?

2021-03-03
Step 1
For the addition of two matrices to be possible, the order of the two matrices should be same.
Step 2 For the given matrices, the order of the matrix A is $$2 \times 3$$ while the order of the matrix B is $$3 \times 2$$. Hence, the orders of matrices A and B are not same and thus, A+B is not possible.

### Relevant Questions

Perform the indicated matrix operations B - A given that A, B, and C are defined as follows. If an operation is not defined, state the reason.
$$A=\begin{bmatrix}4 & 0 \\-3 & 5 \\ 0 & 1 \end{bmatrix} B=\begin{bmatrix}5 & 1 \\-2 & -2 \end{bmatrix} C=\begin{bmatrix}1 & -1 \\-1 & 1 \end{bmatrix}$$
Matrix multiplication is pretty tough- so i will cover that in class. In the meantime , compute the following if
$$A=\begin{bmatrix}2&1&1 \\-1&-1&4 \end{bmatrix} , B=\begin{bmatrix}0 & 2 \\-4 & 1\\2&-3 \end{bmatrix} , C=\begin{bmatrix}6 & -1 \\3 & 0\\-2&5 \end{bmatrix} , D=\begin{bmatrix}2 & -3&4 \\-3& 1&-2 \end{bmatrix}$$
If the operation is not possible , write NOT POSSIBLE and be able to explain why
a)A+B
b)B+C
c)2A
compute the indicated matrices (if possible). D+BC
Let $$A=\begin{bmatrix}3 & 0 \\ -1 & 5 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 1 \\ 0 & 2 &3 \end{bmatrix} , C=\begin{bmatrix}1 & 2 \\ 3 & 4 \\ 5 &6 \end{bmatrix} , D=\begin{bmatrix}0 & -3 \\ -2 & 1 \end{bmatrix} , E=\begin{bmatrix}4 & 2 \end{bmatrix} , F=\begin{bmatrix}-1 \\ 2 \end{bmatrix}$$
compute the indicated matrices (if possible). B - C
Let
$$A=\begin{bmatrix}3 & 0 \\-1 & 5 \end{bmatrix} , B=\begin{bmatrix}4 & -2&1 \\0 & 2&3 \end{bmatrix} , C=\begin{bmatrix}1 & 2 \\3 & 4\\5&6 \end{bmatrix}, D=\begin{bmatrix}0 & -3 \\-2 & 1 \end{bmatrix},E=\begin{bmatrix}4 & 2 \end{bmatrix},F=\begin{bmatrix}-1 \\2 \end{bmatrix}$$
compute the indicated matrices . FE
$$A=\begin{bmatrix}3 & 0 \\-1 & 5 \end{bmatrix} , B=\begin{bmatrix}4 & -2&1 \\0 & 2&3 \end{bmatrix} , C=\begin{bmatrix}1& 2 \\3 & 4\\5&6 \end{bmatrix} , D=\begin{bmatrix}0 & -3 \\-2 & 1 \end{bmatrix} , E=\begin{bmatrix}4 & 2 \end{bmatrix} ,F=\begin{bmatrix}-1 \\2 \end{bmatrix}$$
Let $$u=\begin{bmatrix}2 \\ 5 \\ -1 \end{bmatrix} , v=\begin{bmatrix}4 \\ 1 \\ 3 \end{bmatrix} \text{ and } w=\begin{bmatrix}-4 \\ 17 \\ -13 \end{bmatrix}$$ It can be shown that 4u-3v-w=0. Use this fact (and no row operations) to find a solution to the system Ax=b , where
$$A=\begin{bmatrix}2 & -4 \\5 & 17\\-1&-13 \end{bmatrix} , x=\begin{bmatrix}x_1 \\ x_2 \end{bmatrix} , b=\begin{bmatrix}4 \\ 1 \\ 3 \end{bmatrix}$$
Perform the indicated matrix operations:
$$\begin{bmatrix}5 & 4 \\-3 & 7 \\ 0 & 1 \end{bmatrix}-\begin{bmatrix}-4 & 8 \\6 & 0 \\ -5 & 3 \end{bmatrix}$$
Compute the indicated matrices, if possible .
A^2B
let $$A=\begin{bmatrix}1 & 2 \\3 & 5 \end{bmatrix} \text{ and } B=\begin{bmatrix}2 & 0 & -1 \\3 & -3 & 4 \end{bmatrix}$$
$$A=\begin{bmatrix}-3 & 5 & -6 \\ 3 & -5 & -1 \end{bmatrix} , B=\begin{bmatrix}-6 & 8 & -3 \\ 3 & 6 & -2 \end{bmatrix}$$
a. $$\begin{bmatrix}-30 & 42 & -24 \\ 18 & 14 & -10 \end{bmatrix}$$
c. $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix}$$
d. $$\begin{bmatrix} -9 & 13 & -9 \\ 6 & 1 & -3 \end{bmatrix}$$
c. $$\begin{bmatrix} 18 & -22 & 0 \\ -6 & -34 & 6 \end{bmatrix}$$
$$\begin{bmatrix}1 & 4&3 \\0 & 1&4\\0&0&2 \end{bmatrix}\begin{bmatrix}3 & 2 \\1 & 1\\4&5 \end{bmatrix}$$