Question

# A=begin{bmatrix}1 & -3&3 1 & 0&-2 end{bmatrix} ,B=begin{bmatrix}-3 &1&2 2 & 5&-3 end{bmatrix} Find 2B?

Matrices
$$A=\begin{bmatrix}1 & -3&3 \\1 & 0&-2 \end{bmatrix} ,B=\begin{bmatrix}-3 &1&2 \\2 & 5&-3 \end{bmatrix}$$
Find 2B?

2020-12-06
Step 1
Given Matrices A and B -
$$A=\begin{bmatrix}1 & -3&3 \\1 & 0&-2 \end{bmatrix} ,B=\begin{bmatrix}-3 &1&2 \\2 & 5&-3 \end{bmatrix}$$
2B=?
Rule to multiuply a number with matrices,
Let X be a matrix -
$$X=\begin{bmatrix}a & b&c \\d & e&f \end{bmatrix}$$
Multiplying by m in matix X,
$$mX=m\begin{bmatrix}a & b&c \\d & e&f \end{bmatrix}$$
$$mX=\begin{bmatrix}m \times a & m \times b&m \times c \\m \times d & m \times e&m \times f \end{bmatrix}$$
Hence,
$$2B=2\begin{bmatrix}-3 & 1&2 \\2 & 5&-3 \end{bmatrix}$$
$$2B=\begin{bmatrix}2 \times (-3) & 2 \times (1)&2 \times (2) \\2 \times (2) & 2 \times (5)&2 \times (-3) \end{bmatrix}$$
$$2B=\begin{bmatrix}-6 & 2&4 \\4 & 10&-6 \end{bmatrix}$$
Hence,
$$2B=\begin{bmatrix}-6 & 2&4 \\4 & 10&-6 \end{bmatrix}$$