Explanation Given: The matrix A = [ 4 − 2 2 − 2 4 2 2 2 4 ] Approach: A matrix is a rectangular array of numbers arranged in rows and columns where the element in the i th row and j th column is a i j . Calculation: Evaluating inverse using row reduction [ 4 − 2 2 − 2 4 2 2 2 4 | | | 1 0 0 0 1 0 0 0 1 ] = [ 2 − 1 < To determine (b) To find: The det. A . To determine (c) A nontrivial solution x to A x = 0 . To determine (d) To find: The scalars c 1 , c 2 and c 3 .

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 9.3, Problem 30E

To determine

(a)

To show:

The row-reduction procedure applied to [A⋮I] fails to produce the inverse of A.

To determine

(b)

To find:

The det. A.

To determine

(c)

A nontrivial solution x to Ax=0.

To determine

(d)

To find:

The scalars c1,c2 and c3.

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Chapter 9.3, Problem 29E

Chapter 9.3, Problem 31E

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Chapter 9 Solutions

Fundamentals of Differential Equations and Boundary Value Problems

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(a) To show: The row-reduction procedure applied to [ A ⋮ I ] fails to produce the inverse of A .

Solution Summary: The author explains that the row-reduction procedure applied to left[AIright] fails to produce the inverse of A.

Videos

(a)

To show:

The row-reduction procedure applied to [A⋮I] fails to produce the inverse of A.

(b)

To find:

The det. A.

(c)

A nontrivial solution x to Ax=0.

(d)

To find:

The scalars c1,c2 and c3.

Want to see the full answer?

Chapter 9 Solutions

(a) To show: The row-reduction procedure applied to [ A ⋮ I ] fails to produce the inverse of A .

Solution Summary: The author explains that the row-reduction procedure applied to left[AIright] fails to produce the inverse of A.

Videos

(a) To show: The row-reduction procedure applied to [A⋮I] fails to produce the inverse of A.

(b) To find: The det. A.

(c) A nontrivial solution x to Ax=0.

(d) To find: The scalars c1,c2 and​ c3.

Want to see the full answer?

Chapter 9 Solutions

(a)

To show:

The row-reduction procedure applied to [A⋮I] fails to produce the inverse of A.

(b)

To find:

The det. A.

(c)

A nontrivial solution x to Ax=0.

(d)

To find:

The scalars c1,c2 and c3.