Question

solve the following system of homogeneous equations. x+y-z=0 , x+2y+z=0 , 3x+6y-5z=0

Answer 1

Step-by-step explanation:

Given set of equations,

x+y−z=0

x−2y+z=0

3x+6y−5z=0

Arranging the above equations in form of matrix and finding the coefficient of matrix, we get,

A=

⎣

⎢

⎢

⎡

1

1

3

1

−2

6

−1

1

−5

⎦

⎥

⎥

⎤

R

2

→R

2

−R

1

R

3

→R

3

−3R

1

A∼

⎣

⎢

⎢

⎡

1

0

0

1

−3

3

−1

2

−2

⎦

⎥

⎥

⎤

det(A)=0 as 2nd and 3rd rows are identical.

as, ρ(A)=2, submatrix is [

1

0

1

−3

]

we get,

x+y−z=0

3y−2z=0

Let z=k

y=

3

2k

x=

3

k

or, we have,

x=k,y=2k,z=3k