Solve {l}{8}{2}{1}{lll}{10}&{4}&{-2}

$$\left( \begin{array} { l } { 8 } \\ { 2 } \\ { 1 } \end{array} \right) \left( \begin{array} { l l l } { 10 } & { 4 } & { - 2 } \end{array} \right)$$

Evaluate

$$\left(\begin{matrix}80&32&-16\\20&8&-4\\10&4&-2\end{matrix}\right)$$

Steps Using Matrix Multiplication Rule

Matrix multiplication is defined if the number of columns of the first matrix is equal to the number of rows of the second matrix.

$$\left(\begin{matrix}8\\2\\1\end{matrix}\right)\left(\begin{matrix}10&4&-2\end{matrix}\right)$$

Multiply the first element of the first matrix by the first element of the second matrix to obtain the element in the first row, first column of the product matrix.

$$\left(\begin{matrix}8\times 10&&\\&&\\&&\end{matrix}\right)$$

The remaining elements of the product matrix are found in the same way.

$$\left(\begin{matrix}8\times 10&8\times 4&8\left(-2\right)\\2\times 10&2\times 4&2\left(-2\right)\\10&4&-2\end{matrix}\right)$$

Simplify each element by multiplying the individual terms.

$$\left(\begin{matrix}80&32&-16\\20&8&-4\\10&4&-2\end{matrix}\right)$$

Calculate Determinant

$$0$$