Question

Suppose an 8 x 10 matrix A has eight pivot columns. Is Col A=R8? Is Nul A=R2? Explain your answers. Is Col A =R8? A. Yes. Since A has eight pivot columns, dim Col A is 8. Thus, Col A is an eight-dimensional subspace of R8, so Col A is equal to R8 OB. No, the column space of Ais not R. Since A has eight pivot columns, dim Col A is 0. Thus, Col A is equal to 0. OC. No. Since A has eight pivot columns, dim Col A is 8. Thus, Col A is an eight-dimensional subspace of R8, so Col A is not equal to R8 OD. No, Col A is not R8 Since A has eight pivot columns, dim Col A is 2. Thus, Col A is equal to R2 Is Nul A=R2? O A. No, Nul A is equal to R2. Since A has eight pivot columns, dim Nul A is equal to 0. Thus, Nul A is equal to 0. O B. No, Nul A is not equal to R2. Since A has eight pivot columns, dim Nul A is equal to 8. Thus, Nul A is equal to R O C. Yes, Nul A is equal to R2. Since A has eight pivot columns, dim Nul A is equal to 2. Thus, Nul A is equal to R2 OD. No, Nul A is not equal to R2. It is true that dim Nul A is equal to 2, but Nul A is a subspace of R10

Answer 1

has eight A be 8 x 10 Matrin given pivot Column ColCA)= R8 (A) Yes since A has eight am Col A zs They eight - Dimensional Cola is erues to R² pivot Column Colt is subspace of R² so since to R² المروج is © Yes Ney A A has eight Thus dal A pirot Column Dim alu A zs is eruel to R²

Both the answer is yes