For what value of x, A = [ beginmatrix2(x+1)&2x x&x-2 endmatrix] is a singular matrix?

Question

For what value of x, A = [ beginmatrix2(x+1)&2x x&x-2 endmatrix] is a singular matrix? (A) -2 (B) -3 (C) -1 (D) 0

Tardigrade Admin · Accepted Answer

It is given that A is a singular matrix. ∴ |A|=0 ⇒ | beginmatrix2(x+1)&2x x&x-2 endmatrix|=0 ⇒ 2(x+1)(x-2)-2x2=0 ⇒ 2x2-2x-4-2x2=0 ⇒ 2x+4=0 ⇒ x=-2 qquad qquad

Q. For what value of x, A = $[2 (x + 1) x 2 x x - 2]$ is a singular matrix?

$- 2$

$- 3$

$- 1$

$0$

It is given that $A$ is a singular matrix.
$∴ ∣ A ∣ = 0$
$\Rightarrow ∣ ∣ 2 (x + 1) x 2 x x - 2 ∣ ∣ = 0 \Rightarrow 2 (x + 1) (x - 2) - 2 x^{2} = 0$
$\Rightarrow 2 x^{2} - 2 x - 4 - 2 x^{2} = 0 \Rightarrow 2 x + 4 = 0 \Rightarrow x = - 2$

Q. For what value of x, A = [2(x+1)x​2xx−2​] is a singular matrix?

−2

−3

−1

0

It is given that A is a singular matrix. ∴∣A∣=0 ⇒∣∣​2(x+1)x​2xx−2​∣∣​=0⇒2(x+1)(x−2)−2x2=0 ⇒2x2−2x−4−2x2=0⇒2x+4=0⇒x=−2

Q. For what value of x, A = $[2 (x + 1) x 2 x x - 2]$ is a singular matrix?

$- 2$

$- 3$

$- 1$

$0$

It is given that $A$ is a singular matrix.
$∴ ∣ A ∣ = 0$
$\Rightarrow ∣ ∣ 2 (x + 1) x 2 x x - 2 ∣ ∣ = 0 \Rightarrow 2 (x + 1) (x - 2) - 2 x^{2} = 0$
$\Rightarrow 2 x^{2} - 2 x - 4 - 2 x^{2} = 0 \Rightarrow 2 x + 4 = 0 \Rightarrow x = - 2$