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Q25.

Expert-verified

Algebra 2

Found in: Page 172

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

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

The required matrix is,

$[\begin{matrix} 24 & 16 \\ - 32 & - 5 \\ - 48 & - 11 \end{matrix}]$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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.

$[\begin{matrix} 4 \cdot 6 + 0 \cdot (- 2) & 4 \cdot 4 + 0 \cdot 1 \end{matrix}]$

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.

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

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.

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

Step 4 – Perform simplification of obtained matrix.

$[\begin{matrix} 24 & 16 \\ - 32 & - 5 \\ - 48 & - 11 \end{matrix}]$

Most popular questions for Math Textbooks

For exercises 30 and 31, use the costs for an overnight stay at a hotel that are given below.

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Suite: $$ 75$ weekday; $$ 95$ weekend

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