Home
Class 12
MATHS
Find the value of x for which the matrix...

Find the value of x for which the matrix `A=[(2//x,-1,2),(1,x,2x^(2)),(1,1//x,2)]` is singular.

Text Solution

Verified by Experts

The correct Answer is:
`pm 1`
`A=[(2//x,-1,2),(1,x,2x^(2)),(1,1//x,2)]`
We have
`|A|=(2/x) |(x,2x^(2)),(1//x,2)|+|(1,2x^(2)),(1,2)|+2|(1,x),(1,1//x)|`
`=2/x (0)+2-2x^(2)+2 (1/x-x)`
`=(2x(1-x^(2))+2(1-x^(2)))/(x)`
`=(2(x+1)^(2)(1-x))/(x)`
Now, `|A|=0" "implies" "x= pm 1`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise 13.2|6 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.3|10 Videos

  • MATRICES

    CENGAGE|Exercise Examples|75 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

Find the values of x for which matrix [(3,-1+x,2),(3,-1,x+2),(x+3,-1,2)] is singular.

The value of x, for which the matrix A = [(e^(x-2),e^(7+x)),(e^(2+x),e^(2x+3))] is singular is

For what value of x the matrix A = [(1,-2,3),(1,2,1),(x,2,-3)] is singular.

For what value of x, the matrix A=[(0,1,-2),(-1,0,x^(3)),(2,-3,0)] is skew- symmetric .

Find the value of x for which A= [(e^(2x+1),e^(x-2)),(e^(2-x),e^(x-7))] is singular:

For what value of x , the matrix A = [(0,1,-2),(-1,0,x^3),(2,-3,0)] is skew symmetric

Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

Find the values of x which the function f(x)=sqrt(log_(1//2)((x-1)/(x+5)) is defined.