## Question

###### Suppose 7*11 matrix A has seven pivot columns: Is Col A = R7? Is Nul A = R4? Explain your answers.Is Col A=RT?0 A No_ Since A has seven pivot columns_ dim Col A =7. Thus, Col A is seven-dimensional subspace of R" so Col A is not equal to R7 No, Col A is not R7 Since A has seven pivot columns_ dim Col A =4. Thus, Col A is equal to R4_ Yes. Since A has seven pivot columns, dim Col A=7 Thus Col A is a seven-dimensional subspace of R" Col A is equal to R7. No, the column space of A is not

Suppose 7*11 matrix A has seven pivot columns: Is Col A = R7? Is Nul A = R4? Explain your answers. Is Col A=RT? 0 A No_ Since A has seven pivot columns_ dim Col A =7. Thus, Col A is seven-dimensional subspace of R" so Col A is not equal to R7 No, Col A is not R7 Since A has seven pivot columns_ dim Col A =4. Thus, Col A is equal to R4_ Yes. Since A has seven pivot columns, dim Col A=7 Thus Col A is a seven-dimensional subspace of R" Col A is equal to R7. No, the column space of A is not R7_ Since = A has seven pivot columns, dim Col A =0. Thus Col A is equal to 0_ Is Nul A= R4? OA No, Nul A is equal to R4_ Since A has seven pivot columns, dim Nul A = 0. Thus Nul A is equal to 0. No, Nul A is not equal to R4 It is true that dim Nul A = 4, but Nul A is a subspace of R11_ No, Nul A is not equal to R4 Since A has seven pivot columns dim Nul A=7- Thus, Nul A is equal to R7 _ Yes, Nul A is equal to R4. Since A has seven pivot columns, dim Nul A=4. Thus, Nul A is equal- to R4