For the given matrix A, find k such that Nul A is a subspace of and find m such

Question

For the given matrix A, find k such that Nul A is a subspace of and find m such that Col A is subspace of m A = [4 0 0 -1 1 -7 2 6 -5 -1 0 3 -3 -4 4 -5 5 -3] k = 3, m = 3 k = 6, m = 6 k = 3 m = 6 k = 6 m = 3 Determine if the vector u is in the column space of matrix A and whether it is the space of A. u = [-2 -5 -2], A = [1 -3 4 -1 0 -5 3 -3 6]In Col A and in Nul A In Col A and not in Nul A Not in Col A in Nul A Not in Col A, not in Nul A determine which of the sets of vectors is linearly independent The set {P1, P2 P3} where P1(t) = 1 P2 (t) = t^2 P3(t) = 1 + 5t The set {P1, P2 P3} where P1(t) = 1 P2 (t) = t^2 P3(t) = 2t + 5t^2 The set {P1, P2 P3} where P1(t) = 1 P2 (t) = t^2 P3(t) = 1 + 5t + t^2 C only all of them B only A only A and C determine whether {v_1, v_2, v_3} is a basis for R^3 v_1 = [-2 4 -8], v_2 = [1 0 3], v_3 = [4 -4 14] No Yes slove the problem Let v_1 =[-4 -1 -2], v_2 = [-3 1 -2]v_3 = [1 -5 2]and H = span {v_1 v_2, v_3} Note that v_3 = 2v_1 - 3v_1 which of the following sets form a basis for the subspace H i.e., which sets form an efficient spanning set containing no unnecessary vectors? {v_1, v_2, v_3} {v_1, v_2} {v_1, v_3} {v_2, v_3} B. C and D b and C B only A only

Explanation / Answer

ANswer of question (9)

Here as the order of given matrix is 3 x 6, so by rule Null A is a subspace of R^6 and col A is a subspace of R^3.

So clearly k=6 and m=3 here.

or option D is correct answer.

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