Home
Class 12
MATHS
Find the values of x for which matrix [(...

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

Text Solution

Verified by Experts

Given matrix is singular
`:. |(3,x-1,2),(3,-1,x+2),(x+3,-1,2)|=0`
`implies |(0,x,-x),(3,-1,x+2),(x+3,-1,2)|=0" "[R_(1) rarr R_(1)-R_(2)]`
`implies |(0,x,-x),(-x,0,x),(x+3,-1,2)|=0" "[R_(2) rarr R_(2)-R_(3)]`
`implies |(0,x,0),(-x,0,x),(x+3,-1,1)|=0" "[C_(3) rarr C_(3)+C_(2)]`
`implies -x[(-x)-x(x+3)]=0`
`implies x(x^(2)+4x)=0`
`implies x=0, -4`
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

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

For how many values of x in the closed interval [-4, -1], the matrix [(3,-1+x,2),(3,-1,x+2),(x+3,-1,2)] is singular ?

The values of x for which the given matrix [(-x,x,2),(2,x,-x),(x,-2,-x)] will be non-singular are

Find the value of x if , |{:(3,x),(x,1):}|=|{:(3,2),(4,1):}|

Find the set of values of x for which (tan 3x - tan 2x)/(1 + tan 3x cdot tan 2x) = 1

Find the real values of x for which the function f(x) = cos^(-1) sqrt(x^(2) + 3 x + 1) + cos^(-1) sqrt(x^(2) + 3x) is defined

Find the value of int_0^1 2x^3-3x^2-x+1 3dxdot

Find the value of int_(0)^(1)root(3)(2x^(3)-3x^(2)-x+1)dx .

Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^2+(2p-9)x+6. Find the remaining factor for this value of pdot

CENGAGE PUBLICATION-MATRICES-All Questions
  1. For what values of x and y are the following matrices equal ? A=[(2x...

    Text Solution

    |

  2. For alpha, beta, gamma in R, let A=[(alpha^(2),6,8),(3,beta^(2),9),(...

    Text Solution

    |

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

    Text Solution

    |

  4. If A=[(1,2),(3,4),(5,6)] and B=[(-3,-2),(1,-5),(4,3)], then find D=[(p...

    Text Solution

    |

  5. A=[(cos alpha,-sin alpha),(sin alpha,cos alpha)] and A+A^(T)=I, find t...

    Text Solution

    |

  6. Let A be a square matrix. Then prove that (i) A + A^T is a symmetric m...

    Text Solution

    |

  7. If A=[(2,-1),(3,1)] and B=[(1,4),(7,2)] , find 3A-2B.

    Text Solution

    |

  8. Find non-zero values of x satisfying the matrix equation: x[(2x,2),(3,...

    Text Solution

    |

  9. Let A+2B=[(1,2,0),(6,-3,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,...

    Text Solution

    |

  10. If [(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2)...

    Text Solution

    |

  11. Prove that every square matrix can be uniquely expressed as the sum of...

    Text Solution

    |

  12. Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and 11 - n ...

    Text Solution

    |

  13. If A=[{:(2,3,-1),(1,4,2):}] and B=[{:(2,3),(4,5),(2,1):}] then prove t...

    Text Solution

    |

  14. Find the value of x and y that satisfy the equations [(3,-2),(3,0),(2,...

    Text Solution

    |

  15. Find the values of x ,\ y,\ z if the matrix A=[(0,2y,z), (x, y,-z ),...

    Text Solution

    |

  16. If A =[[costheta,sintheta],[-sintheta,costheta]] then prove that A^n=[...

    Text Solution

    |

  17. If A=((p,q),(0,1)), then show that A^(8)=((p^(8),q((p^(8)-1)/(p-1))),(...

    Text Solution

    |

  18. Let A=[(2,1),(0,3)] be a matrix. If A^(10)=[(a,b),(c,d)] then prove th...

    Text Solution

    |

  19. Show that the solutions of the equation [(x,y),(z,t)]^2=0 are[(x,y),(...

    Text Solution

    |

  20. Let A be square matrix. Then prove that A A^(T) and A^(T) A are symmet...

    Text Solution

    |