Thread: matrix

(a) Suppose that the augmented matrix for a system of equations reduces to
row1 1 0 0 0 -1
row2 0 1 0 0 2
row3 0 0 1 0 0
row4 0 0 0 1 -4
:
Write the solution if the variables are x; y; z and w, respectively.

(b)What is the solution to the system in (a) if the second row is replaced by
0 0 0 0 1 ?
(c) What is the solution to the system in (a) if the second row is replaced by
0 0 0 0 0 ?

Originally Posted by trythis

(a) Suppose that the augmented matrix for a system of equations reduces to
row1 1 0 0 0 -1
row2 0 1 0 0 2
row3 0 0 1 0 0
row4 0 0 0 1 -4
:
Write the solution if the variables are x; y; z and w, respectively.

(b)What is the solution to the system in (a) if the second row is replaced by
0 0 0 0 1 ?
(c) What is the solution to the system in (a) if the second row is replaced by
0 0 0 0 0 ?

a) is easy

$\displaystyle x = -1, y = 2, z = 0, w = -4$.

b) is nonsense because then you get $\displaystyle w = 2$ and $\displaystyle w = 4$ at the same time. You also don't get anything for y.

c) Gives the same answers for x, z and w, but y is arbitrary.