Home
Class 12
MATHS
If A=[1 2x0 1 0 0 0 1] and B=[1-2y0 1 0 ...

If `A=[1 2x0 1 0 0 0 1]` and `B=[1-2y0 1 0 0 0 1]` and `A B=I_3` , then `x+y` equals (a) 0 (b) -1 (c) 2 (d) none of these

Text Solution

Verified by Experts

Given: `A=[(1, 2,x),(0, 1, 0),( 0, 0, 1)]` and `B=[(1,-2,y),(0, 1, 0),( 0, 0, 1)]`
And `AB=I_3`
Now
`|A|=|(1, 2,x),(0, 1, 0),( 0, 0, 1)|=1`
`|B|=|(1,-2,y),(0, 1, 0),( 0, 0, 1)|=1`
`implies A=B^(-1)........(i)`
Then
...
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

If {:A=[(1,2,x),(0,1,0),(0,0,1)]andB=[(1,-2,y),(0,1,0),(0,0,1)]:} and AB=I_3 , then x + y equals

If x<0,\ y<0 such that x y=1 , then tan^(-1)x+tan^(-1)y equals pi/2 (b) -pi/2 (c) pi (d) none of these

If [[x,1]][[1,0],[2,0]]=0 ,then x equals (A) 0 (B) -2 (C) -1 (D) 2

Let A d+2B=[1 2 0 6-3 3-5 3 1]a n d2A-B=[2-1 5 0-1 6 0 1 2] . Then T r(B) has the value equal to 0 b. 1 c. 2 d. none

int_0^oo (xlogx)/(1+x^2)^2dx= (A) e (B) 1 (C) 0 (D) none of these

If f(x)={xsin1/x , x!=0 0, x=0 , then (lim)_(x->0)f(x) equals a. 1 b . 0 c. -1 d. none of these

If [(2x+y,0),(5,x)] = [(5,0),(5,3)] then y is equal to (a) 1 (b) 3 (c) 2 (d) -1

Q.4 If A= [[0,1,-2],[-1,0,5],[2,5,0]] , then (a)A'=A (b)A'=-A (c)A'=2A (d) None of these

If (x+iy)^(1/3)=a+ib, then (x)/(a)=(y)/(b)=0b1c.-1d .none of these

If f(x)=(x+1)^(cot x) be continuous at x=0, the f(0) is equal to 0( b) (1)/(e)(c)e(d) none of these

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a1,a2,a3),(b1,b2,b3),(c1,c2...

    Text Solution

    |

  2. If A=[(1,a),(0, 1)] , then A^n (where n in N) equals [(1,n a),(0,...

    Text Solution

    |

  3. If A=[1 2x0 1 0 0 0 1] and B=[1-2y0 1 0 0 0 1] and A B=I3 , then x+y e...

    Text Solution

    |

  4. If A=[1-1 2-1] , B=[a1b-1] and (A+B)^2=A^2+B^2 , then values of a and ...

    Text Solution

    |

  5. If A=[alphabetagamma-alpha] is such that A^2=I , then 1+alpha^2+betaga...

    Text Solution

    |

  6. If S=[S(i j)] is a scalar matrix such that s(i i)=ka n dA is a square ...

    Text Solution

    |

  7. If a square matrix such that A^2=A , then (I+A)^3-7A is equal to A ...

    Text Solution

    |

  8. If a matrix A is both symmetric and skew-symmetric, then A is a

    Text Solution

    |

  9. The matrix [(0, 5,-7),(-5, 0, 11),( 7,-11, 0)] is (a) a skew-symmetr...

    Text Solution

    |

  10. If A is a square matrix, then A A is a (a) skew-symmetric matrix (b)...

    Text Solution

    |

  11. If A and B are symmetric matrices, then A B A is (a) symmetric m...

    Text Solution

    |

  12. If A=[(5,x),( y,0)] and A=A^T , then

    Text Solution

    |

  13. If A is 3xx4 matrix and B is a matrix such that A^T B and B A^T are bo...

    Text Solution

    |

  14. If A=[a(i j)] is a square matrix of even order such that a(i j)=i^2...

    Text Solution

    |

  15. If A=[costheta-sinthetasinthetacostheta] , then A^T+A=I2 , if theta=np...

    Text Solution

    |

  16. If A=[(2, 0,-3),( 4, 3, 1),(-5, 7, 2)] is expressed as the sum of a s...

    Text Solution

    |

  17. Out of the following matrices, choose that matrix which is a scalar...

    Text Solution

    |

  18. The number of all possible matrices of order 3xx3 with each entry 0...

    Text Solution

    |

  19. Which of the given values of x and y make the following pairs ...

    Text Solution

    |

  20. If A=[(0, 2),( 3,-4)] and k A=[(0, 3a),(2b, 24)] , then the values o...

    Text Solution

    |