Question

Simplify ax-y+¹ az-x+¹ ay-z+¹​

Answer 1

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1

Determinant of Coefficient Matrix ,

⎣

⎢

⎢

⎡

a

1

1

1

a

1

1

1

a

⎦

⎥

⎥

⎤

=0

a(a

2

−1)−1(a−1)+1(1−a)=0

a

3

−a−a+1+1−a=0

a

3

−3a+2=0⇒ If a=1

a=1∣

1

0

0

1

−3

1

2

−2

|______________

1

1

−2

0

a

2

+a−2=0⇒a

2

+2a−a−2=0

a(a+2)−1(a+2)=0

a=−2,1

a is either −2 (or) 1

Answer 2

${\huge{\pink{↬}}} \:  \: {\huge{\underline{\boxed{\bf{\pink{Answer}}}}}}$

Determinant of Coefficient Matrix ,

⎣

⎢

⎢

⎡

a

1

1

1

a

1

1

1

a

⎦

⎥

⎥

⎤

=0

a(a

2

−1)−1(a−1)+1(1−a)=0

a

3

−a−a+1+1−a=0

a

3

−3a+2=0⇒ If a=1

a=1∣

1

0

0

1

−3

1

2

−2

|______________

1

1

−2

0

a

2

+a−2=0⇒a

2

+2a−a−2=0

a(a+2)−1(a+2)=0

a=−2,1

a is either −2 (or) 1