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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 61 (page 756)

In Problems 61鈥� 66, show that each matrix has no inverse.
$[\begin{array}{l} 4 & 2 \\ 2 & 1 \end{array}]$

Short Answer

Expert verified

The given matrix has no inverse.

Step by step solution

01

Step 1. Given information

A matrix is given as,

$[\begin{array}{l} 4 & 2 \\ 2 & 1 \end{array}]$

02

Step 2. Finding the inverse.

To find the inverse,

$[A 鈭� I_{2}] = [\begin{array}{l} 4 & 2 & 1 & 0 \\ 2 & 1 & 0 & 1 \end{array}] R_{1} = \frac{1}{4} r_{1}, R_{2} = r_{2} - 2 r_{1} [\begin{array}{l} 4 & 2 & 1 & 0 \\ 2 & 1 & 0 & 1 \end{array}] 鈫� [\begin{matrix} 1 & \frac{1}{2} & \frac{1}{4} & 0 \\ 2 & 1 & 0 & 1 \end{matrix}] 鈫� [\begin{matrix} 1 & \frac{1}{2} & \frac{1}{4} & 0 \\ 0 & 0 & - \frac{1}{2} & 1 \end{matrix}]$

Since the left side does not represent an identity matrix, therefore, inverse does not exist.

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