A matrix is given in row-echelon form.

Question

A matrix is given in row-echelon form.

	1	2	3	−1	7
0	1	−2	0	5
0	0	1	2	5
0	0	0	1	3

(a) Write the system of equations for which the given matrix is the augmented matrix. (Enter each answer in terms of x, y, z, and w.)

			=	7
		=	5
		=	5
		=	3

(b) Use back-substitution to solve the system.

(x, y, z, w) =

 

 

Answer 1

x + 2y + 3z - w = 7

y - 2z = 5

z + 2w = 5

w = 3

(x, y, z ,w) = (7, 3, -1, 3)