Linear Algebra Examples

$x ([\begin{array}{c} a \\ b \\ d \end{array}]) = [\begin{array}{c} 2 a - b + 5 d \\ - 4 a + 2 b - 10 d \end{array}]$ , $[\begin{array}{c} 4 \\ 4 \\ 1 \end{array}]$

Step 1

Apply the transformation to the vector.

$[\begin{array}{c} 2 (4) - (4) + 5 (1) \\ - 4 \cdot 4 + 2 (4) - 10 \cdot 1 \end{array}]$

Step 2

Simplify each element in the matrix.

Tap for more steps...

Rearrange $2 (4) - (4) + 5 (1)$ .

$[\begin{array}{c} 9 \\ - 4 \cdot 4 + 2 (4) - 10 \cdot 1 \end{array}]$

Rearrange $- 4 \cdot 4 + 2 (4) - 10 \cdot 1$ .

$[\begin{array}{c} 9 \\ - 18 \end{array}]$