Home
Class 12
MATHS
Compute A^(-1) for the following matrix ...

Compute `A^(-1)` for the following matrix `A=[(-1,2,5),(2,-3,1),(-1,1,1)]`. Hence solve the system of equations `-x+2y+5z=2, 2x-3y+z=15` & `-x+y+z= -3`

Text Solution

Verified by Experts

The correct Answer is:
`A^(-1)=-(1)/(7)[(-4,3,17),(-3,4,11),(-1,-1,-1)]` & `x=2,y=-3, z=2`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MOTION|Exercise Exercise - 3(Comprehension - based Questions)|3 Videos
  • MATRICES

    MOTION|Exercise Exercise - 3(Matrix Match - type Questions)|1 Videos
  • MATRICES

    MOTION|Exercise Exercise - 2(Level-II) (Multiple correct Option - type Questions)|7 Videos
  • LIMIT

    MOTION|Exercise EXERCISE-4|17 Videos
  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 4 (LEVEL - II)|17 Videos

Similar Questions

Explore conceptually related problems

Find the inverse of matrix A=[[1,1,1],[2,-1,-1],[0,2,1]] hence solve the system of linear equations : x+y+z=2 2x-y-z=4 2y+z=1

If A=[{:(1,1,1),(1,0,2),(3,1,1):}] , find A^(-1) . Hence, solve the system of equations : x+y+z=6 , x+2z=7 , 3x+y+z=12

If A=[[1,3,4],[2,1,2],[5,1,1]] , find A^(-1) . Hence solve the system of equations : x+3y+4z=8, 2x+y+2z=5 and 5x+y+z=7

If A=[{:(3,1,2),(3,2,-3),(2,0,-1):}] , find A^(-1) . Hence, solve the system of equations : 3x+3y+2z=1 , x+2y=4 , 2x-3y-z=5

If matrix A=[[2,3,1],[1,2,2],[-3,1,-1]] Find A^(-1) and hence solve the system of equation 2x+y-3z=13,3x+2y+z=4,x+2y-z=8

If matrix A=|[2,3,1],[1,2,2],[-3,1,-1]| Find A^(-1) and hence solve the system of equation 2x+y-3z=13,3x+2y+z=4,x+2y-z=8

Solve the system of equations by cramer's rule: 2x-3y+z=-1 ,3x+y-2z=1 and 4x-y+z=9

If A=[[1,-1,12,1,-31,1,1]], find A^(-1) and hence solve the system of linear equation.x+2y+z=4,-x+y+z=0,x-3y+z=2

If matrix A=[[2,1,-3],[3,2,1],[1,2,-1]] . Find A^(-1) and hence solve the system of equation 2x+y–3z=13, 3x+2y+z=4, x+2y-z=8

If A=((2,-3,5),(3,2,-4),(1,1,-2)) find A^(-1). Use it to solve the system of equations 2x-3y+5z=11 , 3x+2y-4z=-5 and x+y-2z=-3

MOTION-MATRICES -Exercise - 3(Subjective - type Questions)
  1. For the matrix A=[{:(,3,2),(,1,1):}] Find a & b so that A^(2)+aA+bI=0....

    Text Solution

    |

  2. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

    Text Solution

    |

  3. If {1/2(A-A'+1)}^-1=2/lambda[(lambda-13,-lambda/3,lambda/3),(-17,10,-...

    Text Solution

    |

  4. Given A=[[2,0,-alpha],[5,alpha,0],[0,alpha,3]] For a in R-{a, b}, A^(-...

    Text Solution

    |

  5. Compute A^(-1) for the following matrix A=[(-1,2,5),(2,-3,1),(-1,1,1)...

    Text Solution

    |

  6. For the matrix A=[(4,-4,5),(-2,3,-3),(3,-3,4)] find A^(-2) .

    Text Solution

    |

  7. Gaurav purchases 3 pens, 2 bags and 1 instrument box and pays Rs. 41. ...

    Text Solution

    |

  8. Solve the following system of linear equations by using the principle ...

    Text Solution

    |

  9. Solve the following system of linear equations by using the principle ...

    Text Solution

    |

  10. By using the principle of matrix, show that the following system of eq...

    Text Solution

    |

  11. Find the number of 2xx2 matrix satisfying (i) aij is 1 or -1 (ii) ...

    Text Solution

    |

  12. If A = [[0, 1],[3,0]]and (A^(8) + A^(6) + A^(4) + A^(2) + I) V= [[0],[...

    Text Solution

    |

  13. If the matrices A=[(1,2),(3,4)] and B=[(a,b),(c,d)] (a,b,cd not all si...

    Text Solution

    |

  14. If [a b c1-a] is an idempotent matrix and f(x)=x-^2=b c=1//4 , then th...

    Text Solution

    |

  15. If the matrix A is involutary, show that (1)/(2)(I+A) and (1)/(2)(I-A)...

    Text Solution

    |

  16. A(3xx3) is a matrix such that |A|-a,R=(adj A) such that |B|=b. Find...

    Text Solution

    |

  17. Use matrix to solve the following system of equations. x+y+z=3 x+...

    Text Solution

    |

  18. Use matrix to solve the following system of equations. x+y+z=6 x-y...

    Text Solution

    |

  19. Use matrix to solve the following system of equations. x+y+z=3 x+2...

    Text Solution

    |

  20. Use matrix to solve the following system of equations. x+y+z=3 x+...

    Text Solution

    |