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(1 pt) This question pertains to the four subspaces related to a matrix. The mat

ID: 2961965 • Letter: #

Question

(1 pt) This question pertains to the four subspaces related to a matrix. The material is covered in section 2.7. Select all statement(s) that are correct. There may be more than one correct answer. A. The null space of a matrix is the same as the null space of the related matrix obtained by row reduction . B. The kernel and null space of a matrix are the same thing. C. To find a basis of the columns space of a matrix we take the columns that correspond to pivots in the row reduced matrix. D. To find a basis of the row space of a matrix we take the nonzero rows of the related row reduced matrix. E. The dimension of the row space plus the dimension of the null space of an n x m matrix is n. F. The row space of a matrix is the same as the row space of the related matrix obtained by row reduction . G. The column space of a matrix is the same as the column space of the related matrix obtained by row reduction . H. The dimension of the row space plus the dimension of the null space of an n x m matrix is m. I. The left null space of a matrix is the same as the left space of the related matrix obtained by row reduction . J. To find a basis of the row space of a matrix we take the rows that correspond to pivots in the row reduced matrix. K. The row rank and column rank of a matrix are the same.

Explanation / Answer


B. The kernel and null space of a matrix are the same thing

C. To find a basis of the columns space of a matrix we take the columns that correspond to pivots in the row reduced matrix.

. F. The row space of a matrix is the same as the row space of the related matrix obtained by row reduction .


H. The dimension of the row space plus the dimension of the null space of an n x m matrix is m


J. To find a basis of the row space of a matrix we take the rows that correspond to pivots in the row reduced matrix


K.The row rank and column rank of a matrix are the same..