Suppose a 5×7 matrix A has five pivot columns. Is Col A = R⁵ Is Nul A=R². Explain your answers.
Is Col A =R⁵
A. No, the column space of A is not R⁵. Since A has five pivot columns, dim Col A is 0. Thus, Col A is equal to 0. O
B. Yes. Since A has five pivot columns, dim Col A is 5. Thus, Col A is a five-dimensional subspace of R⁵, so Col A is equal to R⁵. O
C. No, Col A is not R⁵. Since A has five pivot columns, dim Col A is 2. Thus, Col A is equal to R²
D. No. Since A has five pivot columns, dim Col A is 5. Thus, Col A is a five-dimensional subspace of R⁵, so Col A is not equal to R⁵