Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.
5. $[\begin{matrix} 0 & 2 & 3 & 4 \\ 0 & 0 & 0 & 4 \\ 1 & 2 & 3 & 4 \\ 0 & 0 & 3 & 4 \end{matrix}]$

Therefore, the determinant of given matrix is given by,

$d e t A = - 24$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition

Gaussian elimination method is used to solve a system of linear equations.

Gaussian elimination provides a relatively efficient way of constructing the inverse to a matrix.

Interchanging two rows. Multiplying a row by a constant (any constant which is not zero).

Step 2: Given

Given Matrix,

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

Step 3: To find determinant by using Gaussian Eliminations

First, we switch the first and third row.

We get,

$A_{1} = [\begin{matrix} 1 & 2 & 3 & 4 \\ 0 & 0 & 0 & 4 \\ 0 & 2 & 3 & 4 \\ 0 & 0 & 3 & 4 \end{matrix}]$

Then, we switch the second and third row.

We get,

$A_{2} = [\begin{matrix} 1 & 2 & 3 & 4 \\ 0 & 2 & 3 & 4 \\ 0 & 0 & 0 & 4 \\ 0 & 0 & 3 & 4 \end{matrix}]$

Lastly, we switch the third and fourth row.

We get

$A_{3} = [\begin{matrix} 1 & 2 & 3 & 4 \\ 0 & 2 & 3 & 4 \\ 0 & 0 & 3 & 4 \\ 0 & 0 & 3 & 4 \end{matrix}]$

We had three row interchanges, so

$\begin{array}{l} d e t A = {(- 1)}^{3} . 1.2.3.4 \\ de t A = - 24 . \end{array}$

Find Study Materials for

Create Study Materials

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.
5. $[\begin{matrix} 0 & 2 & 3 & 4 \\ 0 & 0 & 0 & 4 \\ 1 & 2 & 3 & 4 \\ 0 & 0 & 3 & 4 \end{matrix}]$

Step by Step Solution

Step 1: Definition

Step 2: Given

Step 3: To find determinant by using Gaussian Eliminations

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.5. [0234000412340034]

Step by Step Solution

Step 1: Definition

Step 2: Given

Step 3: To find determinant by using Gaussian Eliminations

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.
5. $[\begin{matrix} 0 & 2 & 3 & 4 \\ 0 & 0 & 0 & 4 \\ 1 & 2 & 3 & 4 \\ 0 & 0 & 3 & 4 \end{matrix}]$