Question

If A=[2sec−1x−1cosec−1x] is a singular matrix then find the value of x

Answer 1

Given, A=

⎣

⎢

⎢

⎡

1

1

x

−2

2

2

3

1

−3

⎦

⎥

⎥

⎤

∵ Matrix A is singular then,

∣A∣=0

⇒

∣

∣

∣

∣

∣

∣

∣

∣

1

1

x

−2

2

2

3

1

−∣∣∣∣∣∣∣∣=0

⇒(−6−2)+2(−3−x)+3(2−2x)=0

⇒−8−6−2x+6−6x=0

⇒−8−x=0

⇒x= −88

⇒x=−1

⇒ Hence,x=−1