Precalculus Examples

$[\begin{array}{c} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}] \cdot [\begin{array}{c} - 1 & 2 \\ 2 & 3 \\ 1 & 0 \end{array}] - [\begin{array}{c} 7 & 6 \\ 8 & 5 \end{array}]$

Multiply each row in the first matrix $[\begin{array}{c} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}]$ by each column in the second matrix $[\begin{array}{c} - 1 & 2 \\ 2 & 3 \\ 1 & 0 \end{array}]$ .

$[\begin{array}{c} 1 \cdot - 1 + 2 \cdot 2 + 3 \cdot 1 & 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 0 \\ 4 \cdot - 1 + 5 \cdot 2 + 6 \cdot 1 & 4 \cdot 2 + 5 \cdot 3 + 6 \cdot 0 \end{array}] - [\begin{array}{c} 7 & 6 \\ 8 & 5 \end{array}]$

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

$[\begin{array}{c} 6 & 8 \\ 12 & 23 \end{array}] - [\begin{array}{c} 7 & 6 \\ 8 & 5 \end{array}]$

Subtract the corresponding elements of $[\begin{array}{c} 7 & 6 \\ 8 & 5 \end{array}]$ from each element of $[\begin{array}{c} 6 & 8 \\ 12 & 23 \end{array}]$ .

$[\begin{array}{c} 6 - 7 & 8 - 6 \\ 12 - 8 & 23 - 5 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 6 - 7 & 8 - 6 \\ 12 - 8 & 23 - 5 \end{array}]$ .

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Simplify $6 - 7$ .

$[\begin{array}{c} - 1 & 8 - 6 \\ 12 - 8 & 23 - 5 \end{array}]$

Simplify $8 - 6$ .

$[\begin{array}{c} - 1 & 2 \\ 12 - 8 & 23 - 5 \end{array}]$

Simplify $12 - 8$ .

$[\begin{array}{c} - 1 & 2 \\ 4 & 23 - 5 \end{array}]$

Simplify $23 - 5$ .

$[\begin{array}{c} - 1 & 2 \\ 4 & 18 \end{array}]$

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