Matrix scalar multiplication

When multiplying a matrix by a scalar (a single number), we multiply each element of the matrix by that scalar.

For a 2x2 matrix, this can be written as:

k \begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} k a & k b \\ k c & k d \end{bmatrix}

Examples

multiply each element of the matrix by 2:
- Top-left: 2 \times 1 = 2
- Top-right: 2 \times 3 = 6
- Bottom-left: 2 \times 5 = 10
- Bottom-right: 2 \times 7 = 14
So, 2 \times \begin{bmatrix} 1 & 3 \\ 5 & 7 \end{bmatrix} = \begin{bmatrix} 2 & 6 \\ 10 & 14 \end{bmatrix}
Answer: \begin{bmatrix} 2 & 6 \\ 10 & 14 \end{bmatrix}

Question	Answer
How do you multiply a matrix by a scalar?	Multiply each element of the matrix by that scalar.
What is the result of 2 \times \begin{bmatrix} 1 & 3 \\ 5 & 7 \end{bmatrix}?	\begin{bmatrix} 2 & 6 \\ 10 & 14 \end{bmatrix}
How do you evaluate k \begin{bmatrix} a & b \\ c & d \end{bmatrix} for scalar k?	\begin{bmatrix} k a & k b \\ k c & k d \end{bmatrix}
What are the steps to evaluate 2 \times \begin{bmatrix} 1 & 3 \\ 5 & 7 \end{bmatrix}?	Multiply each element by 2: - Top-left: 2 \times 1 = 2 - Top-right: 2 \times 3 = 6 - Bottom-left: 2 \times 5 = 10 - Bottom-right: 2 \times 7 = 14 Result: \begin{bmatrix} 2 & 6 \\ 10 & 14 \end{bmatrix}