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T1. It can be proved that a nonzero matrix A has rank k if and only if some k x k submatrix has a nonzero determinant and all square submatrices of larger size have determinant zero. Use this fact to find the rank of [3 -1 3 2 51 5 -3 2 3 4 A = 1 -5 0 -7 -3 7 -5 1 4 1 Check your result by computing the rank of A in a different way.

T1. It can be proved that a nonzero matrix A has rank k if and only if some k x k submatrix has a nonzero determinant and all square submatrices of larger size have determinant zero. Use this fact to find the rank of [3 -1 3 2 51 5 -3 2 3 4 A = 1 -5 0 -7 -3 7 -5 1 4 1 Check your result by computing the rank of A in a different way.

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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T1. It can be proved that a nonzero matrix A has rank k if and only if some k x k submatrix has a nonzero determinant and all square submatrices of larger size have determinant zero. Use this fact to find the rank of [3 -1 3 2 51 5 -3 2 3 4 A = 1 -3 -5 -7 [7 -5 1 4 1. Check your result by computing the rank of A in a different way.
Transcribed Image Text:T1. It can be proved that a nonzero matrix A has rank k if and only if some k x k submatrix has a nonzero determinant and all square submatrices of larger size have determinant zero. Use this fact to find the rank of [3 -1 3 2 51 5 -3 2 3 4 A = 1 -3 -5 -7 [7 -5 1 4 1. Check your result by computing the rank of A in a different way.
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