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In this question A is an n x n matrix. (a) State, and describe fully, a formula that allows the determinant of A to be calculated. (b) By treating the matrix A as an active transformation matrix, or otherwise, explain why the determinant of a matrix vanishes when the vectors formed by its columns are linearly dependent.

In this question A is an n x n matrix. (a) State, and describe fully, a formula that allows the determinant of A to be calculated. (b) By treating the matrix A as an active transformation matrix, or otherwise, explain why the determinant of a matrix vanishes when the vectors formed by its columns are linearly dependent.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In this question A is an n x n matrix. (a) State, and describe fully, a formula that allows the determinant of A to be calculated. (b) By treating the matrix A as an active transformation matrix, or otherwise, explain why the determinant of a matrix vanishes when the vectors formed by its columns are linearly dependent.
Transcribed Image Text:In this question A is an n x n matrix. (a) State, and describe fully, a formula that allows the determinant of A to be calculated. (b) By treating the matrix A as an active transformation matrix, or otherwise, explain why the determinant of a matrix vanishes when the vectors formed by its columns are linearly dependent.
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