33. A = 148 8-3 -7 -1 27 3 4 -2 29 5 5 3 6 9 -5 -2 1 480 5 0250 0001 4 0000 0 50-1

A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. A = 57 64 23 3 - 26 4 2 - 12 14 Find a basis for Col A. 1 2 3 014 0 0 0 10 - 8 0

Determine whether the statement below is true or false. Justify the answer. Here, A is an mxn matrix. The dimension of Col A is the number of pivot columns in A. Choose the correct answer below. O A. The statement is true. The pivot columns of A form a basis for Col A. Therefore, the number of pivot columns of A is the same as the dimension of Col A. O B. The statement is false. The number of pivot columns determines the dimension of the null space, not the column space. C. The statement is false. The dimension of Col A cannot be determined without the size of matrix A. O D. The statement is true. The number of pivot columns is equal to the number of free variables in the equation Ax = 0. The number of free variables in Ax = 0 is equal to the dimension of the column space.

Find a basis for col(A) and nul(A) and state the dimension of each. -2-7 -3 9 A = 2 -6 4 8 3 -9-2 2