Simplify the Matrix 3[[2x,-4y],[x+1,3y-2]]

$3 [\begin{array}{c} 2 x & - 4 y \\ x + 1 & 3 y - 2 \end{array}]$

Step 1

Substitute in each matrix definition.

$3 [\begin{array}{c} 2 x & - 4 y \\ x + 1 & 3 y - 2 \end{array}]$

Step 2

Multiply $3$ by each element of the matrix.

$[\begin{array}{c} 3 \cdot (2 x) & 3 \cdot (- 4 y) \\ 3 \cdot x + 1 & 3 \cdot (3 y) - 2 \end{array}]$

Step 3

Simplify each element in the matrix.

Rearrange $3 \cdot (2 x)$ .

$[\begin{array}{c} 6 x & 3 \cdot (- 4 y) \\ 3 \cdot x + 1 & 3 \cdot (3 y) - 2 \end{array}]$

Rearrange $3 \cdot (- 4 y)$ .

$[\begin{array}{c} 6 x & - 12 y \\ 3 \cdot x + 1 & 3 \cdot (3 y) - 2 \end{array}]$

Rearrange $3 \cdot x + 1$ .

$[\begin{array}{c} 6 x & - 12 y \\ 3 x + 1 & 3 \cdot (3 y) - 2 \end{array}]$

Rearrange $3 \cdot (3 y) - 2$ .

$[\begin{array}{c} 6 x & - 12 y \\ 3 x + 1 & 9 y - 2 \end{array}]$