b 3 pts Which matrices have the same null space as A c 3 pts

(b) (3 pts) Which matrices have the same null space as A?

(c) (3 pts) Which matrices have the same norm as A?

(d) (3 pts) Which matrices have the same rank as A?

Solution

Row echelon form means that Gaussian elimination has operated on the rows and column echelon form means that Gaussian elimination has operated on the columns. In other words, a matrix is in column echelon form if its transpose is in row echelon form.

here is the example for t he RREF matrix of (1 0 a₁ 0 b_1,0 1 a₂ 0 b₂,0 0 0 1 b₃)

(a) matrix Q has the same range as A

matrix Q of (1 0 0 0 0,0 1 1 0 1,0 0 0 1 2)

(b)matrix V has the null space V(0 0 0 ,0 1 0,0 1 1)

(c)matrix L is norm of A(1 0 0 0,0 1 0 0,0 0 0 1)

(d)matrix U hassa rank (1 2 1,2 3 1,1 1 2)has rank=3 asme as A