Q. 38 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. 38 (page 756)

In Problems $31 - 40$ , each matrix is nonsingular. Find the inverse of each matrix.
$[\begin{matrix} 1 & 0 & 2 \\ - 1 & 2 & 3 \\ 1 & - 1 & 0 \end{matrix}]$

Short Answer

Expert verified

The inverse of the matrix $[\begin{matrix} 1 & 0 & 2 \\ - 1 & 2 & 3 \\ 1 & - 1 & 0 \end{matrix}]$ is, $[\begin{matrix} 3 & - 2 & - 4 \\ 3 & - 2 & - 5 \\ - 1 & 1 & 2 \end{matrix}]$ .

Step by step solution

Step 1. Given information

$[\begin{array}{r} 1 & 0 & 2 \\ - 1 & 2 & 3 \\ 1 & - 1 & 0 \end{array}]$

We have to find the inverse of the given matrix.

Step 2. First find the augmented matrix A|I3

$[A | I_{3}] 鈫� [\begin{matrix} 1 & 0 & 2 & 1 & 0 & 0 \\ - 1 & 2 & 3 & 0 & 1 & 0 \\ 1 & - 1 & 0 & 0 & 0 & 1 \end{matrix}]$

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

$[\begin{matrix} 1 & 0 & 2 & 1 & 0 & 0 \\ - 1 & 2 & 3 & 0 & 1 & 0 \\ 1 & - 1 & 0 & 0 & 0 & 1 \end{matrix}] 鈫� \{R_{2} 鈫� R_{2} + R_{1}; R_{3} 鈫� R_{3} - R_{1}\} [\begin{matrix} 1 & 0 & 2 & 1 & 0 & 0 \\ 0 & 2 & 5 & 1 & 1 & 0 \\ 0 & - 1 & - 2 & - 1 & 0 & 1 \end{matrix}] 鈫� \{R_{2} 鈫� R_{2} + R_{3}\} [\begin{matrix} 1 & 0 & 2 & 1 & 0 & 0 \\ 0 & 1 & 3 & 0 & 1 & 1 \\ 0 & - 1 & - 2 & - 1 & 0 & 1 \end{matrix}] 鈫� \{R_{3} 鈫� R_{3} + R_{2}\} [\begin{matrix} 1 & 0 & 2 & 1 & 0 & 0 \\ 0 & 1 & 3 & 0 & 1 & 1 \\ 0 & 0 & 1 & - 1 & 1 & 2 \end{matrix}] 鈫� \{R_{1} 鈫� R_{1} - 2 R_{3}; R_{2} 鈫� R_{2} - 3 R_{3}\} [\begin{matrix} 1 & 0 & 0 & 3 & - 2 & - 4 \\ 0 & 1 & 0 & 3 & - 2 & - 5 \\ 0 & 0 & 1 & - 1 & 1 & 2 \end{matrix}]$

Step 3. The augmented matrix A|I3 is now in the reduced echelon form and the identity matrix I3 is on the left side of the vertical bar and A-1 is on the right side of the vertical bar.

$A^{- 1} = [\begin{matrix} 3 & - 2 & - 4 \\ 3 & - 2 & - 5 \\ - 1 & 1 & 2 \end{matrix}]$ .

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91影视

In Problems $31 - 40$ , each matrix is nonsingular. Find the inverse of each matrix.
$[\begin{matrix} 1 & 0 & 2 \\ - 1 & 2 & 3 \\ 1 & - 1 & 0 \end{matrix}]$

Short Answer

Step by step solution

Step 1. Given information

Step 2. First find the augmented matrix A|I3

Step 3. The augmented matrix A|I3 is now in the reduced echelon form and the identity matrix I3 is on the left side of the vertical bar and A-1 is on the right side of the vertical bar.

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91影视

In Problems 31-40, each matrix is nonsingular. Find the inverse of each matrix.102-1231-10

Short Answer

Step by step solution

Step 1. Given information

Step 2. First find the augmented matrix A|I3

Step 3. The augmented matrix A|I3 is now in the reduced echelon form and the identity matrix I3 is on the left side of the vertical bar and A-1 is on the right side of the vertical bar.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Decision Maths

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems $31 - 40$ , each matrix is nonsingular. Find the inverse of each matrix.
$[\begin{matrix} 1 & 0 & 2 \\ - 1 & 2 & 3 \\ 1 & - 1 & 0 \end{matrix}]$