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

Evaluate 2 \times \begin{bmatrix} 1 & 3 \\ 5 & 7 \end{bmatrix}

• 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}