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Found in: Page 172

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# Find each product, if possible.$\left[\begin{array}{cc}4& 0\\ -3& 7\\ -5& 9\end{array}\right]\cdot \left[\begin{array}{cc}6& 4\\ -2& 1\end{array}\right]$

The required matrix is,

$\left[\begin{array}{cc}24& 16\\ -32& -5\\ -48& -11\end{array}\right]$

See the 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 perform addition between the multiplications to form the first row of product matrix.

$\left[\begin{array}{cc}4\cdot 6+0\cdot \left(-2\right)& 4\cdot 4+0\cdot 1\end{array}\right]$

## Step 2 – Make the second row of product matrix

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

$\left[\begin{array}{cc}4\cdot 6+0\cdot \left(-2\right)& 4\cdot 4+0\cdot 1\\ \left(-3\right)\cdot 6+7\cdot \left(-2\right)& \left(-3\right)\cdot 4+7\cdot 1\end{array}\right]$

## Step 3 – Make the third row of product matrix

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

$\left[\begin{array}{cc}4\cdot 6+0\cdot \left(-2\right)& 4\cdot 4+0\cdot 1\\ \left(-3\right)\cdot 6+7\cdot \left(-2\right)& \left(-3\right)\cdot 4+7\cdot 1\\ -5\cdot 6+9\cdot \left(-2\right)& \left(-5\right)\cdot 4+9\cdot 1\end{array}\right]$

## Step 4 –  Perform simplification of obtained matrix.

$\left[\begin{array}{cc}24& 16\\ -32& -5\\ -48& -11\end{array}\right]$