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(a) If A is an m x n matrix, then rank(A) + nullity(4¹) = m. TRUE FALSE (b) If A is a diagonalizable matrix of ordern, then it has linearly independent eigenvectors. TRUE FALSE (c) Let B= ((1.1.-1). (7.1.-9). (-2.1.3)). Then B forms a basis for R³. TRUE FALSE (d) If A is an invertible nx matrix, then the row vectors of A are linearly dependent. TRUE FALSE (e) The vector spaces P, and M₂2 are isomorphic. TRUE FALSE

(a) If A is an m x n matrix, then rank(A) + nullity(4¹) = m. TRUE FALSE (b) If A is a diagonalizable matrix of ordern, then it has linearly independent eigenvectors. TRUE FALSE (c) Let B= ((1.1.-1). (7.1.-9). (-2.1.3)). Then B forms a basis for R³. TRUE FALSE (d) If A is an invertible nx matrix, then the row vectors of A are linearly dependent. TRUE FALSE (e) The vector spaces P, and M₂2 are isomorphic. TRUE FALSE

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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(a) If A is an m x n matrix, then rank(4) + nullity(AT) = m. TRUE FALSE (b) If A is a diagonalizable matrix of order , then it has a linearly independent eigenvectors. TRUE FALSE (c) Let B= ((1.1.-1). (7. 1.-9).(-2.1.3)). Then B forms a basis for R³. TRUE FALSE (d) If A is an invertible n x matrix, then the n row vectors of A are linearly dependent. TRUE FALSE (e) The vector spaces P, and M₂2 are isomorphic. TRUE FALSE
Transcribed Image Text:(a) If A is an m x n matrix, then rank(4) + nullity(AT) = m. TRUE FALSE (b) If A is a diagonalizable matrix of order , then it has a linearly independent eigenvectors. TRUE FALSE (c) Let B= ((1.1.-1). (7. 1.-9).(-2.1.3)). Then B forms a basis for R³. TRUE FALSE (d) If A is an invertible n x matrix, then the n row vectors of A are linearly dependent. TRUE FALSE (e) The vector spaces P, and M₂2 are isomorphic. TRUE FALSE
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