Q. 36 In Problems 31-40, each matrix i... [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. 36 (page 756)

In Problems $31 - 40$ , each matrix is nonsingular. Find the inverse of each matrix.
$[\begin{array}{l} b & 3 \\ b & 2 \end{array}] b 鈮� 0$

Short Answer

Expert verified

The inverse of the matrix $[\begin{array}{l} b & 3 \\ b & 2 \end{array}] b 鈮� 0$ is, $[\begin{matrix} \frac{- 2}{b} & \frac{3}{b} \\ 1 & - 1 \end{matrix}]$ .

Step by step solution

Step 1. Given information

$[\begin{array}{l} b & 3 \\ b & 2 \end{array}] b 鈮� 0$

We have to find the inverse of the given matrix.

Step 2. First find the augmented matrix A|I3.

$[A | I_{3}] 鈫� [\begin{array}{l} b & 3 & 1 & 0 \\ b & 2 & 0 & 1 \end{array}]$

Now transform it into $[I_{3} | A^{- 1}]$ using the row transformations.

$[\begin{array}{l} b & 3 & 1 & 0 \\ b & 2 & 0 & 1 \end{array}] 鈫� \{R_{2} 鈫� R_{2} - R_{1}\} [\begin{matrix} b & 3 & 1 & 0 \\ 0 & - 1 & - 1 & 1 \end{matrix}] 鈫� \{R_{1} 鈫� \frac{R_{1}}{b}\} [\begin{matrix} 1 & \frac{3}{b} & \frac{1}{b} & 0 \\ 0 & - 1 & - 1 & 1 \end{matrix}] 鈫� \{R_{2} 鈫� - R_{2}\} [\begin{matrix} 1 & \frac{3}{b} & \frac{1}{b} & 0 \\ 0 & 1 & 1 & - 1 \end{matrix}] 鈫� \{R_{1} 鈫� R_{1} - \frac{3}{b} R_{2}\} [\begin{matrix} 1 & 0 & - \frac{2}{b} & \frac{3}{b} \\ 0 & 1 & 1 & - 1 \end{matrix}]$

Step 3. The augmented matrix A|In is now in the reduced row echelon form and the identity matrix src="data:image/svg+xml;base64,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" role="math" localid="1647448841999" I2 is on the left side of the vertical bar and A-1 is on the right side of the vertical bar.

$A^{- 1} = [\begin{matrix} - \frac{2}{b} & \frac{3}{b} \\ 1 & - 1 \end{matrix}]$ .

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91影视

In Problems $31 - 40$ , each matrix is nonsingular. Find the inverse of each matrix.
$[\begin{array}{l} b & 3 \\ b & 2 \end{array}] b 鈮� 0$

Short Answer

Step by step solution

Step 1. Given information

Step 2. First find the augmented matrix A|I3.

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91影视

In Problems 31-40, each matrix is nonsingular. Find the inverse of each matrix.b3b2b鈮�0

Short Answer

Step by step solution

Step 1. Given information

Step 2. First find the augmented matrix A|I3.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In Problems $31 - 40$ , each matrix is nonsingular. Find the inverse of each matrix.
$[\begin{array}{l} b & 3 \\ b & 2 \end{array}] b 鈮� 0$