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 n terms of the parameter t.) [1 0 0 0 1 1 0 0 0] x1= __________x2 =____________ x3=___________

Answer 1

Answer:

x₁ = 0, x₂ = -t, x₃ = t

Step-by-step explanation:

consider

m = no. of non zero rows in reduced echelon form = 2

n = no. of unknowns = 3

Using the fact that

m < n ⇒ solution is non-trivial

As last row is zero so we can say  x₃ is a free variable i.e

                                             x₃  = t

From second row:

                       $x_{2]+x_{3}=0\\x_{2]=-x_{3}\\x_{2]=-t$

From first row

                                            x₁ = 0