Solve the homogeneous linear system corresponding to the given coefficient matrix. [1 0 0 1]
[0 0 1 0]
[0 0 0 0]

(x1, x2, x3, x4) =

This question is incomplete, the complete question is;

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, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)

[1 0 0 1]

[0 0 1 0]

[0 0 0 0]

(x1, x2, x3, x4) =________

the solution for the given system is; ( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )

Step-by-step explanation:

Given the data in the question;

coefficient matrix

Now, from linear system;

So, with the matrix, the associated equation is;

x₁ + x₄ = 0, x₃ = 0

Number of variables is 4 and ranked of the matrix is 2,

Hence, there are infinite solutions,

There are also two free variables;

from the question,

Let x₄ = t and x₂ = s be the free variables

so

x₁ + x₄ = 0

x₁ + t = 0

x₁ = -t

Therefore, the solution for the given system is;

( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )