Finite Math Examples

$A^{t} b = [\begin{array}{c} 2 & 3 \\ 1 & - 1 \end{array}] [\begin{array}{c} 1 & 0 & - 1 \\ 2 & 3 & 1 \end{array}]$

Step 1

Assuming that $X$ is the matrix to solve for, multiply the inverse matrix by both sides of the equation.

Step 2

Simplify the right side of the equation.

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Multiply each row in the first matrix by each column in the second matrix.

$x = [\begin{array}{c} 2 \cdot 1 + 3 \cdot 2 & 2 \cdot 0 + 3 \cdot 3 & 2 \cdot - 1 + 3 \cdot 1 \\ 1 \cdot 1 - 1 \cdot 2 & 1 \cdot 0 - 1 \cdot 3 & 1 \cdot - 1 - 1 \cdot 1 \end{array}]$

Simplify each element of the matrix by multiplying out all the expressions.

$x = [\begin{array}{c} 8 & 9 & 1 \\ - 1 & - 3 & - 2 \end{array}]$

The matrix is in the most simplified form.

$x = [\begin{array}{c} 8 & 9 & 1 \\ - 1 & - 3 & - 2 \end{array}]$