Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

8. $[\begin{matrix} 0 & 0 & 0 & 0 & 2 \\ 1 & 0 & 0 & 0 & 3 \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 1 & 6 \end{matrix}]$

Therefore, the determinant of given matrix is given by,

$\det A = 2$

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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,

$A_{1} = [\begin{matrix} 0 & 0 & 0 & 0 & 2 \\ 1 & 0 & 0 & 0 & 3 \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 1 & 6 \end{matrix}]$

Step 3: To find determinant by using Gaussian Eliminations

We do row interchanges in the following order: first and second row, second and third row, third and fourth row, fourth and fifth row.

Eventually, we get the matrix

$A_{1} = [\begin{matrix} 0 & 0 & 0 & 0 & 3 \\ 1 & 0 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 1 & 6 \\ 0 & 0 & 0 & 0 & 2 \end{matrix}]$

We had two row interchanges, so

$\det A = {(- 1)}^{4} . 1.1.1.1.2 \det A = 2$

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Linear Algebra With Applications

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Short Answer

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

8. $[\begin{matrix} 0 & 0 & 0 & 0 & 2 \\ 1 & 0 & 0 & 0 & 3 \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 1 & 6 \end{matrix}]$

Step by Step Solution

Step 1: Definition

Step 2: Given

Step 3: To find determinant by using Gaussian Eliminations

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Linear Algebra With Applications

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Short Answer

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10. 8. [0000210003010040010500016]

Step by Step Solution

Step 1: Definition

Step 2: Given

Step 3: To find determinant by using Gaussian Eliminations

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Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

8. $[\begin{matrix} 0 & 0 & 0 & 0 & 2 \\ 1 & 0 & 0 & 0 & 3 \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 1 & 6 \end{matrix}]$