Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, do the following.

Question

Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, do the following. (Use x₁, x₂, x₃, and x₄ as your variables, each representing the columns in turn.)

	0	1	0	1	4
0	0	1	−5	5
0	0	0	0	0
0	0	0	0	0

(a) Determine whether the system has a solution.

(b) Find the solution or solutions to the system, if they exist. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)

Answer 1

The result is NOT the identity matrix, so there are infinitely many solutions.

the equations that survive are

x2 +x4 = 4

x3 - 5*x4 = 5

So for free var x4, x2 = 4 - x4 and x3 = 5(x4+1)

we need the original equations to write x1 in terms of x4