This is linear algebra.
Assume that A is row equivalent to R. A = [1 2 1 3 2 4 2 6 -5 -5 0 -5 11 15 4 19 -3 2 5 -2], R = [1 0 0 0 2 0 0 0 0 5 0 0 4 -7 0 0 5 8 -9 0] Using A and R above, (a) Find the column space for A and R. (b) Find the row space for A and R. (c) Find the nullspace for A and R. (d) What is the dimension of the column space of A, i.e. dim C(A) =? (e) What is the dimension of the row space of A, i.e. dim C(A^T)=? (f) What is the dimension of the nullspace of A, i.e. dim N(A) =? (g) What is the dimension of the nullspace of A^T, i.e. dim N(A^T) =?
Show transcribed image text Assume that A is row equivalent to R. A = [1 2 1 3 2 4 2 6 -5 -5 0 -5 11 15 4 19 -3 2 5 -2], R = [1 0 0 0 2 0 0 0 0 5 0 0 4 -7 0 0 5 8 -9 0] Using A and R above, (a) Find the column space for A and R. (b) Find the row space for A and R. (c) Find the nullspace for A and R. (d) What is the dimension of the column space of A, i.e. dim C(A) =? (e) What is the dimension of the row space of A, i.e. dim C(A^T)=? (f) What is the dimension of the nullspace of A, i.e. dim N(A) =? (g) What is the dimension of the nullspace of A^T, i.e. dim N(A^T) =?