Question

Find each product, if possible.

$\left[\begin{array}{c}5\\ 8\end{array}\right]\cdot \left[\begin{array}{ccc}3& -1& 4\end{array}\right]$

Short answer

The required matrix is,

$\left[\begin{array}{ccc}15& -5& 20\\ 24& -8& 32\end{array}\right]$

Step-by-step solution

Step 1- Make the first row of product matrix

Write the multiplication of first row of first matrix and each column of second matrix and form the first row of product matrix.

$\left[\begin{array}{ccc}5\cdot 3& 5\cdot (-1)& 5\cdot 4\\ & & \end{array}\right]$

– Make the second row of product matrix

Write the multiplication of second row of first matrix and each column of second matrix and form the second row of product matrix

$\left[\begin{array}{ccc}5\cdot 3& 5\cdot (-1)& 5\cdot 4\\ 8\cdot 3& 8\cdot (-1)& 8\cdot 4\end{array}\right]$

Step 3- Write the actual product matrix

Perform simplification of obtained matrix.

$\left[\begin{array}{ccc}15& -5& 20\\ 24& -8& 32\end{array}\right]$