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Question

Solve the following systems of homogeneous linear equations by matrix method:
x+y6z=0
xy+2z=0
3x+y+2z=0

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Solution

Given set of equations,

x+y6z=0

xy+2z=0

3x+y+2z=0

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

A=116112312

R2R2R1

R3R3+3R1

A1160280416

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

as, ρ(A)=2, submatrix is [1102]

we get,

x+y6z=0

2y+8z=0

Let z=k

y=4k

x=2k

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