If the system of equations 3 x-y+4 z=3, x+2 y-3 z=-2, 6 x+5 y+\\lambdaz= 3 has at least one solution then \lambda=

NIMCET 2021 Question Paper with solutions

Question : 32 of 120

Marks: +1, -0

If the system of equations

3 x-y+4 z=3, x+2 y-3 z=-2,

6 x+5 y+\λz=

3 has at least one solution then

\lambda=

Solution:

|{A}|=0

|\table 3 , -1 , 4 ; 1 , 2, -3 ;6, 5 , \λ |=0

3(2 \λ+15)+1(\λ+18)+4(-7)=0

6 \λ+45+\λ+18=28

7 \λ+35=0

\λ=-5

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