Question

Perform the following operations on matrices (1 8 0 7) (7 6 7 4) = ( )

Answer 1

`\left[\begin{array}{cc}63&38\\49&28\end{array}\right]`

Explanation:

`\left[\begin{array}{cc}1&8\\0&7\end{array}\right]\left[\begin{array}{cc}7&6\\7&4\end{array}\right]=\left[\begin{array}{cc}(1)(7)+(8)(7)&(1)(6)+(8)(4)\\(0)(7)+(7)(7)&(0)(6)+(7)(4)\end{array}\right]\\\\=\left[\begin{array}{cc}63&38\\49&28\end{array}\right]`

Each element of the product matrix is the dot product of the corresponding row in the left matrix and the corresponding column in the right matrix.

For example, the element at row 2, column 1 of the product is [0 7]·[7, 7], the dot product of row 2 of the left matrix with column 1 of the right matrix.

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Many calculators, spreadsheets, and web sites can do this tedious math for you.