Question

Help me understand what Multiplying matrices are. also give an example problem.

Answer 1

If we are multiplying two matrices A and B of order 2X3 and 3X2 respectively, then order of obtained matrix is 2X2.

The matrix is multiplied such that row element of one matrix is multiplied with column element of second matrix. Consider the example of two matrices,

`A=\begin{bmatrix}{1} & {2} & \\ {3} & {4} & {} \\ {} & {} & {}\end{bmatrix}`

And

`B=\begin{bmatrix}{3} & {4} & {} \\ {5} & {6} & {} \\ {} & {} & {}\end{bmatrix}`

Evaluate the product of two matrices AB.

`\begin{gathered} A\cdot B=\begin{bmatrix}{1} & {2} & {} \\ {3} & {4} & {} \\ {} & & {}\end{bmatrix}\cdot\begin{bmatrix}{3} & {4} & {} \\ {5} & {6} & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{1\cdot3+2\cdot5} & {1\cdot4+2\cdot6} & {} \\ {3\cdot3+4\cdot5} & {3\cdot4+4\cdot6} & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{13} & {16} & {} \\ {29} & {36} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}`

We multiply row elements 1 and 2 of matrix A with column element 3 and 5 of matrix B and then add both the obtained numbers.