solve it

Suppose a 3 x9 matrix A has three pivot columns. Is Col A = RS? Is Nul A = R? Explain your answers. Is Col A = R*? Explain your answer. Choose the correct answer and reasoning below. A. No, because a 3x9 matrix exists in RY. If its pivot columns form a 3-dimensional basis, then Col A is isomorphic to R but is not strictly equal to R. O B. Yes, because the column space of a 3 x9 matrix is a subspace of R . There is a pivot in each row, so the column space is 3-dimensional. Since any 3-dimensional subspace of R is R Col A = RS O C. Yes, because there are three pivot columns in A. These columns form a basis in three dimensions. Any 3-dimensional basis spans R3. O D. No, Col A = R. The number of pivot columns is equal to the dimension of the null space. Since the sum of the dimensions of the null space and column space equals the number of columns in the matrix, the dimension of the column space must be 6. Since any 6-dimensional basis is equal to R, Col A = 16