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.
3. $[\begin{matrix} 1 & 3 & 2 & 4 \\ 1 & 6 & 4 & 8 \\ 1 & 3 & 0 & 0 \\ 2 & 6 & 4 & 12 \end{matrix}]$

Therefore, the determinant of given matrix is given by,

$\det A = - 24$

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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,

$A = [\begin{matrix} 1 & 3 & 2 & 4 \\ 1 & 6 & 4 & 8 \\ 1 & 3 & 0 & 0 \\ 2 & 6 & 4 & 12 \end{matrix}]$

Step 3: To find determinant by using Gaussian Eliminations

First, we multiply the first row by -1 and add it to the second and third row. Then, we multiply the first row by -2 and add it to the 4th row.

We get,

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

We had zero row swaps, so

$\begin{array}{l} d e t A = {(- 1)}^{0} . 1.3 . - 2.4 \\ de t A = - 24 \end{array}$

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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.
3. $[\begin{matrix} 1 & 3 & 2 & 4 \\ 1 & 6 & 4 & 8 \\ 1 & 3 & 0 & 0 \\ 2 & 6 & 4 & 12 \end{matrix}]$

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 10.3. [13241648130026412]

Step by Step Solution

Step 1: Definition

Step 2: Given

Step 3: To find determinant by using Gaussian Eliminations

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Pure Maths

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.
3. $[\begin{matrix} 1 & 3 & 2 & 4 \\ 1 & 6 & 4 & 8 \\ 1 & 3 & 0 & 0 \\ 2 & 6 & 4 & 12 \end{matrix}]$