Q46. - Algebra 2

Question

What is the product of $\left[\begin{array}{ccc}5& -2& 3\end{array}\right]$and$\left[\begin{array}{cc}1& -2\\ 0& 3\\ 2& 5\end{array}\right]$

A. $\left[\begin{array}{cc}11& -1\end{array}\right]$

B. $\left[\begin{array}{c}11\\ -1\end{array}\right]$

C. $\left[\begin{array}{cc}5& -10\\ 0& -6\\ 6& -15\end{array}\right]$

D. undefined

Step-by-Step Solution

Answer

The correct option is A.

Step 1- Make the first column of product matrix

Write the multiplication of row of first matrix and first column of second matrix and perform addition between the multiplications to form the first column of product matrix. 

$\left[\begin{array}{cc}5\cdot 1+(-2)\cdot 0+3\cdot 2& \end{array}\right]$

Step 2 – Make the second column of product matrix

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

Step 3- Write the actual product matrix

Perform simplification of obtained matrix.

$\left[\begin{array}{cc}11& -1\end{array}\right]$

The obtained matrix is matching with option A so it is the correct option.