Home
Class 11
MATHS
If A=[(cos^(2)alpha,cos alphasin alpha),...

If `A=[(cos^(2)alpha,cos alphasin alpha),(cos alpha sin alpha, sin^(2)alpha)]` and `B=[(cos^(2)beta, cosbeta sinbeta),(cos beta sin beta, sin^(2)beta)]`
are two matrices such that AB is the null matrix, then

A

0

B

multiple of `pi`

C

an odd multiple of `pi//2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Assertion Reason Type|12 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then

lf cos^2 alpha -sin^2 alpha = tan^2 beta , then show that tan^2 alpha = cos^2 beta-sin^2 beta .

The vector cos alpha cos beta hati + cos alpha sin beta hatj + sin alpha hatk is a

Show that: sin^2 alpha + sin^2 beta + 2sinalpha sinbeta cos(alpha+beta)=sin^2 (alpha+beta)

Show that cos ^2 alpha + cos^2 (alpha +Beta) - 2 cos alpha cos betacos (alpha+ beta) =sin^2 beta

If cos^2alpha-sin^2alpha=tan^2beta," then prove that "tan^2alpha=cos^2beta-sin^2beta .

If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))] , then A(alpha, beta)^(-1) is equal to

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

Evaluate : |{:( 0, sin alpha , - cos alpha ), ( - sin alpha , 0 , sin beta) , (cos alpha , -sin beta , 0):}|

OBJECTIVE RD SHARMA ENGLISH-MATRICES-Exercise
  1. If E(theta)=[[cos theta, sin theta] , [-sin theta, cos theta]] then E(...

    Text Solution

    |

  2. If {:E(theta)=[(cos^2 theta,costhetasintheta),(costhetasintheta,sin^2t...

    Text Solution

    |

  3. If A=[(cos^(2)alpha,cos alphasin alpha),(cos alpha sin alpha, sin^(2)a...

    Text Solution

    |

  4. The matrix X in the equation AX=B, such that A={:[(1,3),(0,1)]:}andB={...

    Text Solution

    |

  5. If I=[1 0 0 1] , J=[0 1-1 0] and B=[costhetasintheta-sinthetacostheta]...

    Text Solution

    |

  6. If A is a square matrix such that A A^T=I=A^TA, then A is

    Text Solution

    |

  7. If A is an orthogonal matrix then A^(-1) equals a.A^T b. A c. A^2 ...

    Text Solution

    |

  8. If D=diag(d1,d2,d3,…,dn)" where "d ne 0" for all " I = 1,2,…,n," then ...

    Text Solution

    |

  9. If {:A=[(ab,b^2),(-a^2,-ab)]:}, then A is

    Text Solution

    |

  10. If A is a 3xx3 matrix and B is a matrix such that A^TB and BA^(T) are ...

    Text Solution

    |

  11. Let {:A=[(1,2),(-5,1)]and A^(-1)=xA+yI:}, then the values of x and y a...

    Text Solution

    |

  12. If A and B arę square matrices of same order such that AB = A and BA =...

    Text Solution

    |

  13. The inverse of an invertible symmetric matrix is a symmetric matrix.

    Text Solution

    |

  14. The inverse of a diagonal matrix is a. a diagonal matrix b. a skew sym...

    Text Solution

    |

  15. If A is a symmetric matrixfand n in N, then A^(n) is

    Text Solution

    |

  16. If A is a skew-symmetric matrix and n is odd positive integer, then A^...

    Text Solution

    |

  17. If A is a skew-symmetric matrix and n is odd positive integer, then A^...

    Text Solution

    |

  18. If A is a skew-symmetric matrix and n is odd positive integer, then A^...

    Text Solution

    |

  19. If A = [a(ij)] is a skew-symmetric matrix of order n, then a(ij)=

    Text Solution

    |

  20. If A and B are symmetric matrices of the same order, write whether ...

    Text Solution

    |