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3. You are given the following matrix -4 12 2 7 a)4 points) Find a basis...

3. You are given the following matrix -4 12 2 7 a)4 points) Find a basis for the nullspace of (b) 4 points] Using the columns

3. You are given the following matrix -4 12 2 7 a)4 points) Find a basis for the nullspace of (b) 4 points] Using the columns of A, find a basis for the column space of A (c) [2 points What are the dimensions of these spaces? (d) [2 points] ls the vector u-I1-1 0 ојт in the nullspace of A? Why? (e) [4 points] Is the vector w-17-9 9-9]T İn the column space of A? If so, express w as a A. linear combination of the basis vectors of the column space of A you found in part (b). () [4 points We want to solve the system Ax b, where b bb b b4T. Find conditions on b, b2, bs, and b to guarantee the existence of a solution to Ax b. Will the solution be unique under these conditions?
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