True/False: If the statement is false, you must justify why it is false. (a) For nx m matrices A and B, det (AB) # det (A)det (B). (b) For an m x n matrix A, rank(A) is the dimension of the null space of A. (c) The non-pivot columns of a matrix A form a basis for the column space of A. (d) An m x m determinant is defined by determinants of (m-1) x (m-1) submatrices.

True/False: If the statement is false, you must justify why it is false. (a) For nx m matrices A and B, det (AB) # det (A)det (B). (b) For an m x n matrix A, rank(A) is the dimension of the null space of A. (c) The non-pivot columns of a matrix A form a basis for the column space of A. (d) An m x m determinant is defined by determinants of (m-1) x (m-1) submatrices.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.3: Matrix Algebra

Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...

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