Matrices and Determinants Part 1

Given P=[

1	2	1
−2	3	−4
1	9	−1

] , Here |P|=0 & also given PX = 0
⇒ [

1	2	1
−2	3	−4
1	9	−1

] [

x

y

z

]=0
⇒

x+2y+z=0

−2x+3y−4z=0

x+9y−z=0

} D = 0, so system have infinite many solutions,
By solving these equation
we get x=

−11λ

2

;y=λ;z=

7λ

2

Also given, x2+y2+z2=1
⇒(

−11λ

2

)2+(λ)2+(

7λ

2

)2=1
⇒λ=±

1

√ 121 4 +1+ 49 4

so, there are 2 values of λ.
∴ so, there are 2 solution set of ( x,y, z)