Q. 35 In Problems 31鈥� 40, each matri... [FREE SOLUTION]

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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. 35 (page 756)

In Problems 31鈥� 40, each matrix is non singular. Find the inverse of each matrix.
$[\begin{matrix} 2 & 1 \\ a & a \end{matrix}]$

Short Answer

Expert verified

The inverse of the matrix $[\begin{matrix} 2 & 1 \\ a & a \end{matrix}]$ is $[\begin{matrix} 1 & - \frac{1}{a} \\ - 1 & \frac{2}{a} \end{matrix}]$

Step by step solution

Step 1. Given Information

The matrix $[\begin{matrix} 2 & 1 \\ a & a \end{matrix}]$ is non singular.

Step 2. Form the matrix

$[A I_{2}] = [\begin{matrix} 2 & 1 \\ a & a \end{matrix}] [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

Step 3. Transform equation into reduced row echelon form

$R_{1} 鈫� \frac{1}{2} R_{1} R_{2} 鈫� R_{2} - 2 R_{1} = [\begin{matrix} 1 & \frac{1}{2} \\ 0 & \frac{a}{2} \end{matrix}] [\begin{matrix} \frac{1}{2} & 0 \\ - \frac{a}{2} & 1 \end{matrix}] R_{2} 鈫� \frac{2}{a} R_{2} = [\begin{matrix} 1 & \frac{1}{2} \\ 0 & 1 \end{matrix}] [\begin{matrix} \frac{1}{2} & 0 \\ - 1 & \frac{2}{a} \end{matrix}] R_{1} 鈫� R_{1} - \frac{1}{2} R_{2} = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] [\begin{matrix} 1 & - \frac{1}{a} \\ - 1 & \frac{2}{a} \end{matrix}]$

Step 4. Find the inverse

The inverse of Ais $[\begin{matrix} 1 & - \frac{1}{a} \\ - 1 & \frac{2}{a} \end{matrix}]$

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91影视

In Problems 31鈥� 40, each matrix is non singular. Find the inverse of each matrix.
$[\begin{matrix} 2 & 1 \\ a & a \end{matrix}]$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Form the matrix

Step 3. Transform equation into reduced row echelon form

Step 4. Find the inverse

One App. One Place for Learning.

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91影视

In Problems 31鈥� 40, each matrix is non singular. Find the inverse of each matrix.21aa

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Form the matrix

Step 3. Transform equation into reduced row echelon form

Step 4. Find the inverse

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Calculus

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 31鈥� 40, each matrix is non singular. Find the inverse of each matrix.
$[\begin{matrix} 2 & 1 \\ a & a \end{matrix}]$