Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Use Exercise 31 to find
$d e t [\begin{matrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 & 5 \\ 1 & 4 & 9 & 16 & 25 \\ 1 & 8 & 27 & 64 & 125 \\ 1 & 16 & 81 & 256 & 625 \end{matrix}]$
Do not use technology.

Therefore, the determinant of the given matrix is given by,

$d e t A = 288$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: By using Vandermonde’s Formula.

For $n = 1$ , we have a $2 \times 2$ matrix

$A = [\begin{matrix} 1 & 1 \\ a_{0} & a_{1} \end{matrix}]$

Using Vandermonde's formula, we have

$\underset{}{\prod_{i > j} (a_{i} - a_{j}) = a_{1} - a_{0} = d e t A}$ .

Step 2: To find the determinant.

Let $a_{0} = 1, a_{1} = 2, a_{2} = 3, a_{3} = 4, a_{4} = 5$ .

Now we can use Vandermonde's formula to find this determinant.

We compute,

$\begin{array}{l} d e t A = \prod_{\frac{i, j - 1}{i > j}} (a_{i} - a_{j}) \\ d e t A = (2 - 1) (3 - 1) (4 - 1) (5 - 1) (3 - 2) (4 - 2) (5 - 2) (4 - 3) (5 - 3) (5 - 4) \\ d e t A = 288 \end{array}$

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Linear Algebra With Applications

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Short Answer

Use Exercise 31 to find
$d e t [\begin{matrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 & 5 \\ 1 & 4 & 9 & 16 & 25 \\ 1 & 8 & 27 & 64 & 125 \\ 1 & 16 & 81 & 256 & 625 \end{matrix}]$
Do not use technology.

Step by Step Solution

Step 1: By using Vandermonde’s Formula.

Step 2: To find the determinant.

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Linear Algebra With Applications

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Short Answer

Use Exercise 31 to finddet[1111112345149162518276412511681256625]Do not use technology.

Step by Step Solution

Step 1: By using Vandermonde’s Formula.

Step 2: To find the determinant.

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Use Exercise 31 to find
$d e t [\begin{matrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 & 5 \\ 1 & 4 & 9 & 16 & 25 \\ 1 & 8 & 27 & 64 & 125 \\ 1 & 16 & 81 & 256 & 625 \end{matrix}]$
Do not use technology.