Home
Class 12
MATHS
If X=[[0, 1], [0, 0]] , then prove that...

If `X=[[0, 1], [0, 0]]` , then prove that `(p I+q X)^m=p^m I+m p^(m-1)q X ,AAp ,q in R` ,where I is a two rowed unit matrix and `m in N.`

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 (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

Prove that px^(q - r) + qx^(r - p) + rx^(p - q) gt p + q + r where p,q,r are distinct number and x gt 0, x =! 1 .

If I_(m)=int_(1)^(e)(log_(e)x)^(m)dx , then prove that, I_(m)=e-mI_(m-1)

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

If P={:[(-1,3,5),(1,-3,-5),(-1,3,5)], show that, P^(2)=P hence find matrix Q such that 3P^(2)-2P+Q=I , where I is the unit matrix of order 3.

Show that every square matrix A can be uniquely expressed as P+i Q ,where P and Q are Hermitian matrices.

If M is a 3 xx 3 matrix, where det M=1 and MM^T=1, where I is an identity matrix, prove theat det (M-I)=0.

Applying P.M.I. prove that (1+x)^n gt 1+nx where n is a pos integer and nge2 :xgt(-1)

Applying P.M.I. prove that x^n-y^n is always divisible by x+y where n is a pos. even integer

If m, n in R , then the value of I(m,n)=int_(0)^(1) t^(m)(1+t)^(n)dt is -

CENGAGE PUBLICATION-MATRICES-All Questions
  1. The product of matrices A=[[cos^2theta,sinthetacostheta],[sinthetacost...

    Text Solution

    |

  2. If A ,\ B are square matrices of order 3,\ A is non-singular and A ...

    Text Solution

    |

  3. If X=[[0, 1], [0, 0]] , then prove that (p I+q X)^m=p^m I+m p^(m-1)q ...

    Text Solution

    |

  4. Let omega != 1 be cube root of unity and S be the set of all non-sing...

    Text Solution

    |

  5. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2...

    Text Solution

    |

  6. If P=[[sqrt(3)/2,1/2],[-1/2,sqrt(3)/2]], A=[[1,1],[0,1]] and Q=PAP^T a...

    Text Solution

    |

  7. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  8. If A=|[alpha,2], [2,alpha]| and |A|^3=125 , then the value of alpha ...

    Text Solution

    |

  9. Let A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=...

    Text Solution

    |

  10. A is an involuntary matrix given by A=|[0, 1,-1], [4,-3, 4], [3,-3, 4]...

    Text Solution

    |

  11. If A is a non-singular matrix such that A A^T=A^T A and B=A^(-1)A^T ,...

    Text Solution

    |

  12. Let M and N be two 3xx3 nonsingular skew-symmetric matrices such that ...

    Text Solution

    |

  13. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

    Text Solution

    |

  14. If A=[[i,-i],[-i ,i]] and B=[[1,-1],[-1 ,1]], t hen ,A^8 equals a.4B b...

    Text Solution

    |

  15. If [[2,-1],[1,0],[-3,4]]A=[[-1,-8,-10],[1,-2,-5],[9,22,15]] , then sum...

    Text Solution

    |

  16. If A = 1/ sqrt(3) [[1,1+i],[1-i,1]] then A((A)^T) equals :

    Text Solution

    |

  17. Identify the incorrect statement in respect of two square matrices Aa ...

    Text Solution

    |

  18. If A is a square matrix such that A^2=A , then write the value of 7A-(...

    Text Solution

    |

  19. If A and B are square matrices of order n , then prove that Aa n dB wi...

    Text Solution

    |

  20. Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the fo...

    Text Solution

    |