Home
Class 12
MATHS
Let A be a nxxn matrix such thatA ^(n) =...

Let A be a `nxxn` matrix such that`A ^(n) = alpha A,` where `alpha ` is a
real number different from 1 and - 1. The matrix `A + I_(n)` is

Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE|Exercise PART-II:|28 Videos

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise SELF PRACTIC PROBLEMS|25 Videos

  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

Let A be an nxxn matrix such that A+A^(')=O_(nxxn) then |I+lamdaA^(2)|geM where 3M+1 is __

Let A be a matrix such that A^(k)=0 where k in N(O represent zero matrix) and B is a matrix such that B=|-A then find the inverse of matrix B

Rank of the following (n+1)xx(n+1) matrix,where a is a real number,is

Matrix A is such that A^(2)=2A-I , where I is the identify matrix. Then for n ne 2, A^(n)=

Let A be a non - singular square matrix such that A^(2)=A satisfying (I-0.8A)^(-1)=I-alphaA where I is a unit matrix of the same order as that of A, then the value of -4alpha is equal to

Let P be a non - singular matrix such that I+P+P^(2)+…….P^(n)=O (where O denotes the null matrix), then P^(-1) is

If A is an idempotent matrix satisfying,(I-0.4A)^(-1)=I-alpha A, where I is the unit matrix of the name order as that of A, then th value of |9 alpha| is equal to

Let A=[[a,b],[c,d]] be a 2xx2 real matrix. If A-alphaI is invertible for every real number alpha , then

RESONANCE-MATRICES & DETERMINANT-HLP
  1. If a,b,c are comples number and z=|{:(,0,-b,-c),(,bar(b),0,-a),(,bar(c...

    Text Solution

    |

  2. If f(x)=log(10)x and g(x)=e^(ln x) and h(x)=f [g(x)], then find the va...

    Text Solution

    |

  3. If A=[{:(,1,a),(,0,1):}] then find lim(n-oo) (1)/(n)A^(n)

    Text Solution

    |

  4. "Let" P=[{:(,"cos"(pi)/(9),"sin"(pi)/(9)),(,-"sin"(pi)/(9),"cos"(pi)/(...

    Text Solution

    |

  5. Let A=[{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B=[{:(,2,-1,-1),(,-1,2,-1),(,...

    Text Solution

    |

  6. Let 'A' is (4xx4) matrix such that the sum of elements in each row is ...

    Text Solution

    |

  7. Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]then prove ...

    Text Solution

    |

  8. Let A be a nxxn matrix such thatA ^(n) = alpha A, where alpha is a ...

    Text Solution

    |

  9. Let p and q be real number such that x^(2)+px+q ne0 for every real num...

    Text Solution

    |

  10. Let A,B,C be three 3 xx 3 matrices with real enteries. If BA+BC+AC=1, ...

    Text Solution

    |

  11. If |z(1)|=|z(2)|=1"then prove that" [{:(,z(1),-z(2)),(,bar(z)(2),bar(z...

    Text Solution

    |

  12. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)...

    Text Solution

    |

  13. A=[(a,1,0),(1,b,d),(1,b,c)],B=[(a,1,1),(0,d,c),(f,g,h)],U=[(f),(g),(h)...

    Text Solution

    |

  14. If the system of equations x=cy+bz, y=az+cx and z=bx+ay has a non-zero...

    Text Solution

    |

  15. IfD=d i ag[d1, d2, dn] , then prove that f(D)=d i ag[f(d1),f(d2), ,f(...

    Text Solution

    |

  16. Fiven the matrix A= [[-1,3,5],[1,-3,-5],[-1,3,5]] and X be the solut...

    Text Solution

    |

  17. If q is a characteristic root of an singular matrix A, then prove that...

    Text Solution

    |

  18. If there are three square matrix A, B, C of same order satisfying the...

    Text Solution

    |

  19. If A is non-singular matrix satifying AB-BA=A, then prove that det(B+I...

    Text Solution

    |

  20. If a rank is a number associated with a matrix which is the highest or...

    Text Solution

    |