Home
Class 12
MATHS
If m=[[1,0],[0,1]]and n=[[0,1],[-1,0]], ...

If `m=[[1,0],[0,1]]`and `n=[[0,1],[-1,0]]`, then what is the value of the determinant of `mcostheta- nsintheta`

A

-1

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`m cos theta-n sin theta=[(cos theta,0),(0,cos theta)]-[(0,sintheta),(-sin theta,0)]`
`[(cos theta,-sin theta),(sin theta, cos theta)]`
`det.(m cos theta -n sin theta)=cos^(2)theta-(-sin^(2)theta)`
`=cos^(2)theta+sin^(2)theta=1`.
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    NDA PREVIOUS YEARS|Exercise MCQ|59 Videos

  • PAIR OF STRAIGHT LINES

    NDA PREVIOUS YEARS|Exercise Example|12 Videos

Similar Questions

Explore conceptually related problems

If m=[{:(1,0),(0,1):}] and n=[{:(0,1),(-1,0):}] , then what is the value of the determinant of m cos theta - n sin theta ?

If m=[[1,00,1]] and n=[[0,1-1,0]], then what m cos theta-n sin theta

If [[1,3] , [0,1]] A = [[1,1] , [0,-1]] then find the value of A

If A = ((1,2),(2,3))and = ((1,0),(1,0)) , then what is the value of determinant of AB ?

If [[1,3],[0,1]]A=[[1,1],[0,-1]] then the value of A is

If prod_(r=1)^(n)[[1,r],[0,1]]=[[1,120],[0,1]] then n = ?

If [{:(1,3),(0,1):}]A=[{:(1,-1),(0,1):}] , then what is the matrix A ?

Given A=[{:(1,0),(0,-1):}] and B=[{:(0,1),(1,0):}] Write the value of AB.

What is the largest value of a third order determinant whose elements are 0 or 1 ?

If [[1,0,0],[0,y,0],[0,0,1]][[x],[-1],[z]]=[[1],[2],[1]], then the value of x+y+z is

NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
  1. Let ax^3+bx^2+cx+d =|(x+1,2x,3x),(2x+3,x+1,x), (2-x,3x+4,5x-1)| then w...

    Text Solution

    |

  2. Let ax^3+bx^2+cx+d =|(x+1,2x,3x),(2x+3,x+1,x), (2-x,3x+4,5x-1)| then w...

    Text Solution

    |

  3. If m=[[1,0],[0,1]]and n=[[0,1],[-1,0]], then what is the value of the ...

    Text Solution

    |

  4. If f{x}=[{:(cos x,-sinx,0),(sin x,cos x,0),(" "0," "0,1):}], then whic...

    Text Solution

    |

  5. Which of the following are correct in respect of the system of equatio...

    Text Solution

    |

  6. A=[{:(1,-1),(2,3):}]and B=[{:(2,3),(-1,-2):}], then which of the follo...

    Text Solution

    |

  7. For the system of linear equations 2x+3y+5z=9, 7x+3y-2z=8 and 2x+3y+l...

    Text Solution

    |

  8. For the system of linear equations 2x+3y+5z=9, 7x+3y-2z=8 and 2x+3y+l...

    Text Solution

    |

  9. If A=[(alpha,2),(2,alpha)] and determinant (A^3)=125, then the value ...

    Text Solution

    |

  10. If B is a non-singular matrix and A is a square matrix, then det (B^(-...

    Text Solution

    |

  11. If a != b != c, are value of x which satisfies the equation |(0,x -a...

    Text Solution

    |

  12. If A=[cosalphasinalpha-sinalphacosalpha] , then verify that A^T\ A=I2 ...

    Text Solution

    |

  13. For the system of equaltions : x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4

    Text Solution

    |

  14. A=[{:(x+y," "y),(" "x,x-y):}],B=[{:(3),(-2):}]and C=[{:(4),(-2):}]. If...

    Text Solution

    |

  15. What is the value of the determinant |{:(1," "1," "1),(1,1+xyz," "1),(...

    Text Solution

    |

  16. If |{:(x,y,0),(0,x,y),(y,0,x):}|=0, then which one of the following is...

    Text Solution

    |

  17. Consider the set A of all determinants of order 3 with entries 0 or 1 ...

    Text Solution

    |

  18. If A = [{:(cos theta,sin theta),(-sin theta,cos theta):}] then what is...

    Text Solution

    |

  19. What is the order of the product [x" "y" "z][{:(a,h,g),(h,b,f),(g,f,c)...

    Text Solution

    |

  20. if A=[{:(0,1),(1,0):}],"then"A^(4)=?

    Text Solution

    |