Linear Algebra Examples

$3 x - 2 y = 18$ , $3 x + 4 y = 12$ , $x = 0$ , $y = 0$

Step 1

Find the $A X = B$ from the system of equations.

$[\begin{array}{c} 3 & - 2 \\ 3 & 4 \\ 1 & 0 \\ 0 & 1 \end{array}] \cdot [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 18 \\ 12 \\ 0 \\ 0 \end{array}]$

Step 2

Left multiply both sides of the matrix equation by the inverse matrix.

Step 3

Any matrix multiplied by its inverse is equal to $1$ all the time. $A \cdot A^{- 1} = 1$ .

Step 4

Simplify the left and right side.

$[\begin{array}{c} x \\ y \end{array}] =$

Step 5

Find the solution.

$x =$

$y =$