Question

Homogeneous equations solutions in 3/4matrix

Answer 1

Answer:

system of linear equations,

3x+y−2z=0

x+y+z=0

x−2y+z=0

Arranging the above equations in form of the matrix, we get,

A=

⎣

⎢

⎢

⎡

3

1

1

1

1

−2

−2

1

1

⎦

⎥

⎥

⎤

determinant ∣A∣=

∣

∣

∣

∣

∣

∣

∣

∣

3

1

1

1

1

−2

−2

1

1

∣

∣

∣

∣

∣

∣

∣

∣

=3(1+2)−1(1−1)−2(−2−1)

=3(3)+0−2(−3)

=15



=0

ρ(A)=3

Hence the system has a trivial solution

x=y=z=0 only