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Suppose that 4 3 -225 3 3 -3 2 6 -2 -2 2-1 5 In the following questions you may use the fact that the matrix B is row-e...

Suppose that 4 3 -225 3 3 -3 2 6 -2 -2 2-1 5 In the following questions you may use the fact that the matrix B is row-equival

Suppose that 4 3 -225 3 3 -3 2 6 -2 -2 2-1 5 In the following questions you may use the fact that the matrix B is row-equivalent to A, where 1 0 1 0 1 0 1 -2 0 5 0 0 01 3 (a) Find: the rank of A the dimension of the nullspace of A (b) Find a basis for the nullspace of A. Enter each vector in the form [x1, x2, ...]; and enter your answer as a comma-separated list: for example if your answer is the set 10 20 330 4 40 50 then type "[1, 2, 3, 4, 5], [10, 20, 30, 40, 50]" WITHOUT the quote marks (c) Find a basis for the column space of A. As in part (b), enter each vector in the form [x1, x2, ..; and enter your answer as a comma-separated list. (d) Let the columns of A be denoted by a1, a2, a3, a4, and a5. Which of the following sets is are linearly independent? Select all that apply Note: three submissions allowed for this part. (a1, a2, a3) (a1, a2, a4) | {a1, a3, a5} None of the above
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3-1 2--9 12- O 12 43 2 2 o 36 2. 2 0 3 ooOI o 32- 0 0 0

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