Home
Class 12
MATHS
Let A=[[3x^2], [1], [6x]],B=[a,b,c]and C...

Let `A=[[3x^2], [1], [6x]],B=[a,b,c]`and `C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2x,(x+2)^2],[ 2x,(x+2)^2, 5x^2]]` be three given matrices, where `a ,b ,ca n dx in Rdot` Given that tr(AB)=tr(C). If `f(x)=a x^2+b x+c ,` then the value of `f(1)` is ______.

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

If intx^2dote^(-2x)dx=e^(-2x)(a x^2+b x+c)+d , then the value of |a/(b c)| is______

Let f(x)=x+1/(2x+1/(2x+1/(2x))) Compute the value of f(5) .

If f(x)=ax^(2)+bx+c and f(x - 1) = f(x) + 2x + 1. then find the values of a and b.

If f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the values of a and b.

Let f(x) = x^2+bx+c , where b,c in R. If f(x) is a factor of both x^4+6x^2+25 and 3x^4+4x^2+28x+5 , then the least value of f(x) is

If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]| then coefficient of x in f(x) is (a) -4 (b) -2 (c) -6 (d) 0

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x)) where f(x) is of the form of ax^(2)+bx+c , then the value of f(1) is

Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3], [6x^2-x-2, 6x^2-7x+2, 12x^2-5x-2]|=0.

Given (1-2x+5x^2-10x^3)(1+x)^n=1+a_1x+a_2x^2+.... and that a_1^2=2a_2 , then the value of n is

CENGAGE PUBLICATION-MATRICES-All Questions
  1. Given a matrix A=[(a,b,c),(b,c,a),(c,a,b)], where a, b, c are real pos...

    Text Solution

    |

  2. If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1...

    Text Solution

    |

  3. Let A=[[3x^2], [1], [6x]],B=[a,b,c]and C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2...

    Text Solution

    |

  4. If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h...

    Text Solution

    |

  5. Let A=([a(i j)])(3xx3) be a matrix such that AA^T=4Ia n da(i j)+2c(i j...

    Text Solution

    |

  6. Let A be the set of all 3xx3 skew-symmetri matrices whose entries are ...

    Text Solution

    |

  7. If A=[[0, 1,2],[1,2,3],[3,a,1]]and A^(-1)[[1//2,-1//2,1//2],[-4,3,b],[...

    Text Solution

    |

  8. For two unimodular complex number z1a n dz2 [[barz1, -z2], [barz2, z1...

    Text Solution

    |

  9. If Aa n dB are two non-singular matrices of the same order such that B...

    Text Solution

    |

  10. If A is non-diagonal involuntary matrix, then a. A-I=O b. A+I=O c. A-...

    Text Solution

    |

  11. if A and B are squares matrices such that A^(2006)=O and A B=A+B , the...

    Text Solution

    |

  12. If matrix A is given by A=|[6, 11], [2, 4]| , then the determinant o...

    Text Solution

    |

  13. If A=[(a, b, c), (x, y, z), (p, q, r)], B=[(q,-b, y),(-p, a,-x),(r,-c,...

    Text Solution

    |

  14. If A and B are two non-singular matrices such that A B=C ,t h e n,|B| ...

    Text Solution

    |

  15. If A(alpha,beta)=[cosalphas inalpha0-s inalphacosalpha0 0 0e^(beta)],t...

    Text Solution

    |

  16. If A=[[a+i b, c+i d],[-c+i d, a-i b]] and a^2+b^2+c^2+d^2=1,t h e n ...

    Text Solution

    |

  17. Statement 1: A=[(4,0,4),(2,2,2), (1,2,1)] B^(-1)=[(1,3,3),(1,4,3),(1,3...

    Text Solution

    |

  18. If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],...

    Text Solution

    |

  19. Statement 1: if a ,b ,c ,d are real numbers and A=[a b c d]a n dA^3=O ...

    Text Solution

    |

  20. A 3xx3 matrix given as, a(i j)=(i-j)/(i+2j) cannot be expressed as a s...

    Text Solution

    |