Solving the homogenous linear system

Question

Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x₁, x₂, and x₃ in terms of the parameter t.)

1 0 0

0 1 1

0 0 0

(x1, x2,x3)=( )

Answer 1

Since this is homogeneous, the linear system to be solved is

x₁+0x₂+0x₃ =0

0x₁+x₂+x₃=0.

We can treat x_3 as the free variable t and hence

(x₁,x₂,x₃) =(0,-t,t).