Q. 12 find the inverse of each nonsing... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 12 (page 795)

find the inverse of each nonsingular matrix.
$[\begin{matrix} 1 & - 1 & 1 \\ 2 & 5 & - 1 \\ 2 & 3 & 0 \end{matrix}]$

Short Answer

Expert verified

find the inverse of each nonsingular matrix.

$[\begin{matrix} 3 & 3 & - 4 \\ - 2 & - 2 & 3 \\ - 4 & - 5 & 7 \end{matrix}]$

Step by step solution

Step 1. Given

$B = [\begin{matrix} 1 & - 1 & 1 \\ 2 & 5 & - 1 \\ 2 & 3 & 0 \end{matrix}]$

Step 2. Calculation of Deterrminant

$|\begin{matrix} 1 & - 1 & 1 \\ 2 & 5 & - 1 \\ 2 & 3 & 0 \end{matrix}| = 1 (5 脳 0 - (- 1) 脳 3) - (- 1) (2 脳 0 - (- 1) 脳 2) + (2 脳 3 - 5 脳 2) = 1 (3) + 1 (2) + 1 (- 4) = 3 - 2 - 4 = - 3 t h u s m a t r i x i s n o n - \sin g u l a r$

Step 3. Calculation for Augmented matrix

$[\begin{matrix} 1 & - 1 & 1 & 1 & 0 & 0 \\ 2 & 5 & - 1 & 0 & 1 & 0 \\ 2 & 3 & 0 & 0 & 0 & 1 \end{matrix}] A p p l y i n g r o w t r a n s f o r m a t i o n [\begin{matrix} 1 & - 1 & 1 & 1 & 0 & 0 \\ 2 & 5 & - 1 & 0 & 1 & 0 \\ 2 & 3 & 0 & 0 & 0 & 1 \end{matrix}] \overset{R_{2} - 2 R_{1}}{鈫� [\begin{matrix} 1 & - 1 & 1 & 1 & 0 & 0 \\ 2 & 5 & - 1 & 0 & 1 & 0 \\ 0 & 5 & - 2 & - 2 & 0 & 1 \end{matrix}]} \overset{\frac{R_{2}}{7}}{鈫�} [\begin{matrix} 1 & - 1 & 1 & 1 & 0 & 0 \\ 0 & 1 & - \frac{3}{7} & - \frac{2}{7} & \frac{1}{7} & 0 \\ 0 & 5 & - 2 & - 2 & 0 & 1 \end{matrix}] \overset{R_{1} + R_{2}}{鈫�} [\begin{matrix} 1 & 0 & \frac{4}{7} & \frac{5}{7} & \frac{1}{7} & 0 \\ 0 & 1 & - \frac{3}{7} & - \frac{2}{7} & \frac{1}{7} & 0 \\ 0 & 5 & - 2 & - 2 & 0 & 1 \end{matrix}] \overset{R_{3} - 5 R_{2}}{鈫�} [\begin{matrix} 1 & 0 & \frac{4}{7} & \frac{5}{7} & \frac{1}{7} & 0 \\ 0 & 1 & - \frac{3}{7} & - \frac{2}{7} & \frac{1}{7} & 0 \\ 0 & 0 & \frac{1}{7} & - \frac{4}{7} & - \frac{5}{7} & 1 \end{matrix}] \overset{7 R_{3}}{鈫�} [\begin{matrix} 1 & 0 & \frac{4}{7} & \frac{5}{7} & \frac{1}{7} & 0 \\ 0 & 1 & - \frac{3}{7} & - \frac{2}{7} & \frac{1}{7} & 0 \\ 0 & 0 & 1 & - 4 & - 5 & 7 \end{matrix}] \overset{R_{1} - \frac{4}{7} R_{3}}{鈫�} [\begin{matrix} 1 - \frac{4}{7} (0) & 0 - \frac{4}{7} (0) & \frac{4}{7} - \frac{4}{7} (1) & \frac{5}{7} - \frac{4}{7} (- 4) & \frac{1}{7} - \frac{4}{7} (- 5) & 0 - \frac{4}{7} (7) \\ 0 & 1 & - \frac{3}{7} & - \frac{2}{7} & \frac{1}{7} & 0 \\ 0 & 0 & 1 & - 4 & - 5 & 7 \end{matrix}] \overset{R_{2} + \frac{3}{7} R_{3}}{鈫�} [\begin{matrix} 1 & 0 & 0 & 3 & 3 & - 4 \\ 0 & 1 & 0 & - 2 & - 2 & 0 \\ 0 & 0 & 1 & - 4 & - 5 & 7 \end{matrix}] T h e r e f o r e t h e i n v e r s e i s [\begin{matrix} 3 & 3 & - 4 \\ - 2 & - 2 & 0 \\ - 4 & - 5 & 7 \end{matrix}]$

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91影视

find the inverse of each nonsingular matrix.
$[\begin{matrix} 1 & - 1 & 1 \\ 2 & 5 & - 1 \\ 2 & 3 & 0 \end{matrix}]$

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation of Deterrminant

Step 3. Calculation for Augmented matrix

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91影视

find the inverse of each nonsingular matrix.1-1125-1230

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation of Deterrminant

Step 3. Calculation for Augmented matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Logic and Functions

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

find the inverse of each nonsingular matrix.
$[\begin{matrix} 1 & - 1 & 1 \\ 2 & 5 & - 1 \\ 2 & 3 & 0 \end{matrix}]$