Solve {c}{1}{-2}{5}*{ccc}{2}&{1}&{-3}

$$\left( \begin{array} { c } { 1 } \\ { - 2 } \\ { 5 } \end{array} \right) \times \left( \begin{array} { c c c } { 2 } & { 1 } & { - 3 } \end{array} \right)$$

Evaluate

$$\left(\begin{matrix}2&1&-3\\-4&-2&6\\10&5&-15\end{matrix}\right)$$

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.

$$\left(\begin{matrix}1\\-2\\5\end{matrix}\right)\left(\begin{matrix}2&1&-3\end{matrix}\right)$$

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.

$$\left(\begin{matrix}2&&\\&&\\&&\end{matrix}\right)$$

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

$$\left(\begin{matrix}2&1&-3\\-2\times 2&-2&-2\left(-3\right)\\5\times 2&5&5\left(-3\right)\end{matrix}\right)$$

Simplify each element by multiplying the individual terms.

$$\left(\begin{matrix}2&1&-3\\-4&-2&6\\10&5&-15\end{matrix}\right)$$

Calculate Determinant

$$0$$