-5 15 -4 12 Let A = -3 9. 4 -12 Find k such that Nul(A) is a subspace of R* Find k such that Col(A) is a subspace of R* Let B = -3 -7 -5 4 Find k such that Row(B) is a subspace of IR Find k such that Nul(B) is a subspace of R* 9 1 0 10 2 Let C = 0 2 9 2 9 1 Find k such that Col(C) is a subspace of R* Find k such that Row(C) is a subspace of R*

Let A = Let B= Let C [ L Find k such that Nul(A) is a subspace of R Find k such that Col(A) is a subspace of R² = 4 -12 [ 8 1 Find k such that Row(B) is a subspace of R² = -3 9 -4 12 [ -5 15 k Find k such that Nul(B) is a subspace of R 8 -5 -9 -9 -1 9 -1 0 -1 0-2 0 -2 9 1 L Find k such that Col(C) is a subspace of R¹ Find k such that Row(C) is a subspace of R² -2 9 -1

Which of the following statements are/is TRUE? 6 1 (1) 5 3 is in the subspace of 2 x 2 matrices spanned by the two matrices 2-1 and 3 -4 (ii) The polynomial 1+2t+3t is in the subspace of polynomials of degree at most three spanned by (2t+t-t, -2t+3t,2-3t) 0 1 0. 1 a (iii) is linearly independent for all values of a. -1 '| -1

Suppose a subspace is spanned by the set S of vectors shown below. -{[]} S= Find a subset of S that forms a basis for the subspace, using the method of transforming a matrix to echelon form, where the columns of the matrix represent vectors spanning the subspace. A basis for the subspace is What is the dimension of the subspace?

SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE Through the point P(-2,-7) tangents are drawn to the ellipse 2x² + y² + 2x-3y - 2 = 0; determine the equations of the tangents and the points of tangency +