Q. 11 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. 11 (page 795)

find the inverse of each nonsingular matrix.
$[\begin{matrix} 3 & 2 \\ 5 & 4 \end{matrix}]$

Short Answer

Expert verified

The inverse of the given matrix is

$[\begin{matrix} 2 & - 1 \\ - \frac{5}{2} & \frac{3}{2} \end{matrix}]$

Step by step solution

Step 1. Given

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

Step 2. Calculation of A|I2

Given A as $2 脳 2$ matrix therefore $[A | I_{2}]$ where $I_{2}$ is identity matrix of second order.

$[A | I_{2}] = [\begin{matrix} 3 & 2 & 1 & 0 \\ 5 & 4 & 0 & 1 \end{matrix}]$

Step 3. Calculation for transformation

Transforming matrix $[A | I_{2}]$

$p e r f o r m t h e r o w o p e r a t i o n R_{1} = \frac{1}{3} r_{1} & R_{2} = r_{2} - 5 r_{1} [\begin{matrix} 3 & 2 & 1 & 0 \\ 5 & 4 & 0 & 1 \end{matrix}] 鈫� [\begin{matrix} 1 & \frac{2}{3} & \frac{1}{3} & 0 \\ 5 & 4 & 0 & 1 \end{matrix}] 鈫� [\begin{matrix} 1 & \frac{2}{3} & \frac{1}{3} & 0 \\ 0 & \frac{2}{3} & - \frac{5}{3} & 1 \end{matrix}]$

Step 4. Final Calculation

Perform

$R_{1} = r_{1} - r_{2} & R_{2} = \frac{3}{2} r_{2} [\begin{matrix} 1 & \frac{2}{3} & \frac{1}{3} & 0 \\ 0 & \frac{2}{3} & - \frac{5}{3} & 1 \end{matrix}] 鈫� [\begin{matrix} 1 & 0 & 2 & - 1 \\ 0 & \frac{2}{3} & - \frac{5}{3} & 1 \end{matrix}] 鈫� [\begin{matrix} 1 & 0 & 2 & - 1 \\ 0 & 1 & - \frac{5}{2} & \frac{3}{2} \end{matrix}]$

$T h u s w e s e e t h e i n v e r s e a s [\begin{matrix} 2 & - 1 \\ - \frac{5}{2} & \frac{3}{2} \end{matrix}]$

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91影视

find the inverse of each nonsingular matrix.
$[\begin{matrix} 3 & 2 \\ 5 & 4 \end{matrix}]$

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation of A|I2

Step 3. Calculation for transformation

Step 4. Final Calculation

One App. One Place for Learning.

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91影视

find the inverse of each nonsingular matrix.3254

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation of A|I2

Step 3. Calculation for transformation

Step 4. Final Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

find the inverse of each nonsingular matrix.
$[\begin{matrix} 3 & 2 \\ 5 & 4 \end{matrix}]$