Home
Class 11
MATHS
If A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,...

If `A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,4+5i,2)]`, then show that A is hermitian matrix.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES -EXERCISE - I|47 Videos

  • MATRICES

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES - EXERCISE - II|34 Videos

  • MATRICES

    AAKASH SERIES|Exercise Exercise - 3.9 (Long Answer Questions)|9 Videos

  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

Similar Questions

Explore conceptually related problems

If A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,4+5i,2)] then A is

If A=[(1,2,3),(3,-2,1),(4,2,1)] , then show that A^(3)-23A-40I=0

A=[(1+i,2-3i,4),(7+2i,-i,3-2i)] then the conjugate of A is

A=[(1+i,2-3i,4),(7+2i,-i,3-2i)] , find the conjugate of A.

If A=((2,3),(0,4)) then A^(2)-5I=

If A=[(8,-6,2),(-6,7,-4),(2,-4,3)] then A(A-3I)(A-15I)=

If |{:(6i , -3i , 1) , (4 , 3i , -1) , (20 , 3 , i):}| = x +iy show that x = y = 0

If I = [(1,0),(0,1)] and E = [(0,1),(0,0)] then show that (aI + bE)^(3) = a^(3)I+3a^(2)bE where I is identify matrix of order 2.

If A=[(3,1),(-1,2)] , show that A^(2)-5A+7I=0 .

AAKASH SERIES-MATRICES -ADDITIONAL EXERCISE
  1. If A, B are symmetric matrices of the same order then show that AB-BA ...

    Text Solution

    |

  2. A=[(1+i,2-3i,4),(7+2i,-i,3-2i)], find the conjugate of A.

    Text Solution

    |

  3. If A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,4+5i,2)], then show that A is ...

    Text Solution

    |

  4. If D=|(1,1,1),(1,1+x,1),(1,1,1+y)| for x!=0,y!=0 then D is

    Text Solution

    |

  5. If A=[a(ij)] is a scalar matrix of order nxxn such that a(ij)=k for al...

    Text Solution

    |

  6. If A is a 3xx3 matrix and det(3A)=k(detA) then k=

    Text Solution

    |

  7. If a,b,c are different and |(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(...

    Text Solution

    |

  8. With the usual notation in DeltaABC det|(1,1,1),(sinA,sinB,sinC),(sin^...

    Text Solution

    |

  9. If Delta(1)=|(x,b,b),(a,x,b),(a,a,x)|, Delta(2)=|(x,b),(a,x)| then

    Text Solution

    |

  10. Prove that |{:(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a...

    Text Solution

    |

  11. If a!=p,b!=q,c!=r and |(p,b,c),(a,q,c),(a,b,r)|=0 then the value of P/...

    Text Solution

    |

  12. If a,b,c, are in A.P. then |(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c)|...

    Text Solution

    |

  13. Let the three digit number A28, 3B9,62C, where A,B,C are integers betw...

    Text Solution

    |

  14. If f(x)=|(1+sin^(2)x,cos^(2)x,4sin2x),(sin^(2)x,1+cos^(2)x,4sin2x),(si...

    Text Solution

    |

  15. If |(x(1),y(1),1),(x(2),y(2),1),(x(3),y(3),1)|=|(a(1),b(1),1),(a(2),b(...

    Text Solution

    |

  16. If a,b,c are in G.P. then find the value of |{:(a,b,ax+by),(b,c,bx+cy)...

    Text Solution

    |

  17. If f(x)=|(cosx, x,1),(2sinx,x^(2),2x),(tanx,x,1)| then Lt(xto0)(f'(x))...

    Text Solution

    |

  18. Find the value of |{:(sqrt(13)+sqrt(3),2sqrt(5),sqrt(5)),(sqrt(15)+sqr...

    Text Solution

    |

  19. If a="cos"(4pi)/3+I"sin"(4pi)/3,then |(1,1,1),(1,a,a^(2)),(1,a^(2),a)|...

    Text Solution

    |

  20. If D(r)=|(2^(r-1),2(3^(r-1)),4(5^(4-1))),(x,y,z),(2^(n)-1,3^(n)-1,5^(n...

    Text Solution

    |