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(59) The dimension of the column space of a matrix is equal to the dimension of

ID: 3033651 • Letter: #

Question

(59) The dimension of the column space of a matrix is equal to the dimension of its row space. (60) If U, V, and W are subspaces of R" so is tu 2v 3ur I u E U, v E V and w E W (61) (1,1,1), (1,0, 1), (3, 2, 3) is a basis for R3 (62) If tu, is an orthonormal set of vectors, then u ur and u +2v-3u are orthogonal. (63) The length of the vector (1,2, 2, 4) is 9. (64) There is a 2x3 matrix A and a 3 x2 matrix B such that AB is the identity matrix. (65) If A is a 2 x 3 matrix and B is a 3 x 2 matrix, then BA can not be the identity matrix because N(A)

Explanation / Answer

(59) The statement is True. Dim(Row(A)) = dim(Col(A)) = rank(A).

(60) The statement is True.

(61) The statement is False. The RREF of the matrix with the given vectors as columns has (1,0,0)T, (0,1,0)T and (2,1,0)T as columns.

(62) The statement is True.The dot product of u+v + w and u+2v -3w is 0.

(63) The statement is False. The length is 5.

(64) The statement is False.

(65) The statement is True.