Question

For which values of xis the matrix

`[(3,-1+x,2),(3,-1,x+2),(x+3,-1,2)]` non-invertible?

पर्याय

• - 4, 0

• 2, 0

• 4, 0

• - 2, 0

Answer 1

- 4, 0

Explanation:

For the given matrix to be non-invertible,

`|(3,-1+x,2),(3,-1,x+2),(x+3,-1,2)|` = 0

Applying R₁ → R₁ - R₂ and R₃ → R₃ - R₂, we get

`|(0,x,-x),(3,-1,x+2),(x,0,-x)|` = 0

⇒ - x (- 3x - x² - 2x) - x (x) = 0

⇒ - 3x - x² - 2x + x = 0

⇒ - x² - 4x = 0

⇒ x = 0, - 4