Question

3x0+1x2 + ! 040-2 8] [3 11. The augmented matrix for the linear system of equations in the unknowns a, y, z has reduced row,echelon form given by 1401 0 01 -2 The general solution to this syste is (D) x = 1, y =-2, z = 0 (E) No solution

Answer 1

Solution:

The augmented matrix is

0 4000 1000

Since the rank of the coefficient matrix is same as the rank of the augmented matrix , the system has a solution.

$\small x+4y=1$

$\small z=-2$

Let  $\small y=t$

$\small \therefore x=1-4t$

So, the general solution is

$\small x=1-4t,\: \: y=t,\: \: z=-2$