Simplify the Matrix [[1,2],[3,4]][[-1,2],[1,0]][[5,9,7]][[2,-4],[4,0],[1,7]]

$[\begin{array}{c} 1 & 2 \\ 3 & 4 \end{array}] [\begin{array}{c} - 1 & 2 \\ 1 & 0 \end{array}] [\begin{array}{c} 5 & 9 & 7 \end{array}] [\begin{array}{c} 2 & - 4 \\ 4 & 0 \\ 1 & 7 \end{array}]$

Step 1

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

$[\begin{array}{c} 1 \cdot - 1 + 2 \cdot 1 & 1 \cdot 2 + 2 \cdot 0 \\ 3 \cdot - 1 + 4 \cdot 1 & 3 \cdot 2 + 4 \cdot 0 \end{array}] [\begin{array}{c} 5 & 9 & 7 \end{array}] [\begin{array}{c} 2 & - 4 \\ 4 & 0 \\ 1 & 7 \end{array}]$

Step 2

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

$[\begin{array}{c} 1 & 2 \\ 1 & 6 \end{array}] [\begin{array}{c} 5 & 9 & 7 \end{array}] [\begin{array}{c} 2 & - 4 \\ 4 & 0 \\ 1 & 7 \end{array}]$

Simplify the Matrix [[1,2],[3,4]][[-1,2],[1,0]][[5,9,7]][[2,-4],[4,0],[1,7]]

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