Home
Class 12
MATHS
If plambda^4+qlambda^3+rlambda^2+slambda...

If `plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-1, lambda+3] , [lambda^2+1, 2-lambda, lambda-3] , [lambda^2-3, lambda+4, 3lambda]|` then `t=`

Text Solution

Verified by Experts

Since given relation is an identity it is true for all real values of `lambda`
` |{:(0,,-1,,3),(1 ,,0,,-4),(-3,,4,,0):}|`
which is skew- symmetric determinant.
So t=0
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

If |(a^2+lambda^2, a b+clambda, ca-blambda), (a b-clambda, b^2+lambda^2, b c+a), (ca+blambda, bc-alambda, c^2+lambda^2)| |(lambda, c, -b), (-c,lambda, a), (b,-a,lambda)|=(1+a^2+b^2+c^2)^3 , then he value of lambda is a. 8 b. 27 c. 1 d. -1

If a satisfies vec axx( hat i+2 hat j+ hat k)= hat i- hat k , then vec a is equal to lambda hat i+(2lambda-1) hat j+lambda hat k ,lambda R b. lambda hat i+(1-2lambda) hat j+lambda hat k ,lambda R c. lambda hat i+(2lambda+1) hat j+lambda hat k ,lambda R d. lambda hat i-(1+2lambda) hat j+lambda hat k ,lambda R

If [(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2))]=Alambda^(2)+Blambda+C , where A, B and C are matrices then find matrices B and C.

If lambda = -2, determine the value of |(0,2lambda,1),(lambda^(2),0,3lambda^(2)+1),(-1,6lambda-1,0)| .

If lambda = - 2 , determine the value of |{:(0,2lambda,1),(lambda^(2),0,3lambda^(2)+1),(-1,6lambda-1 ,0):}|

If the rank of the matrix [(lambda,-1,0),(0, lambda,-1),(-1,0,lambda)] is 2, then find lambda .

If A = [(lambda,1),(-1,-lambda)] , then for what value of lambda,A^(2)=0 ?

Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0 possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

If f(x)=lambda|sinx|+lambda^2|cosx|+g(lambda) has a period = pi/2 then find the value of lambda

Portion of asymptote of hyperbola x^2/a^2-y^2/b^2 = 1 (between centre and the tangent at vertex) in the first quadrant is cut by the line y + lambda(x-a)=0 (lambda is a parameter) then (A) lambda in R (B) lambda in (0,oo) (C) lambda in (-oo,0) (D) lambda in R-{0}

CENGAGE-DETERMINANTS-All Questions
  1. If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...

    Text Solution

    |

  2. Statement 1: If b c+q r=c a+r p=a b+p q=-1, t h e n|a p a p b q b q c...

    Text Solution

    |

  3. If f(theta)=|sinthetacosthetasintheta costhetasinthetacostheta costhet...

    Text Solution

    |

  4. If f(theta)=|[sin^2A,cot A,1],[sin^2B,cosB,1],[sin^2C,cosC,1]| , then...

    Text Solution

    |

  5. The roots of the equation |^x Cr^(n-1)Cr^(n-1)C(r-1)^(x+1)Cr^n Cr^n C(...

    Text Solution

    |

  6. Let Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x^2+2a^2, 3x^3+6a^2x] , [3x^2+2...

    Text Solution

    |

  7. The determinant "Delta"=|(a^2+x) ab ac ab (b^2+x) bc ac bc (c^2+...

    Text Solution

    |

  8. If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,t h e nf(2x)-f(x) is d...

    Text Solution

    |

  9. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

    Text Solution

    |

  10. If (x)= |x^2+4x-3 2x+4 13 ...

    Text Solution

    |

  11. If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|...

    Text Solution

    |

  12. Let f (n) = |{:(n,,n+1,,n+2),(.^(n)P(n),,.^(n+1)P(n+1),,.^(n+2)P(n+2)...

    Text Solution

    |

  13. If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e...

    Text Solution

    |

  14. Let x<1, then value of [[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]...

    Text Solution

    |

  15. If f (x) = |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|then

    Text Solution

    |

  16. Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are non...

    Text Solution

    |

  17. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

    Text Solution

    |

  18. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

    Text Solution

    |

  19. If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has com...

    Text Solution

    |

  20. Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),...

    Text Solution

    |

  21. Roots of the equation |x m n1a x n1a b x1a b c1|=0 are independent of ...

    Text Solution

    |