Home
Class 12
MATHS
If A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1...

If `A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1,1),(2,2,1),(1,1,1)], D=[(10),(13),(9)]`, and `CB=D`. Solve the equation `AX=B`.

Text Solution

Verified by Experts

The correct Answer is:
`X=[(1),(-1),(1)]`
Given that `CB=D`. Now,
`AX=B`
or `CAX=CB=D`
or `X=(CA)^(-1)D`
Now, `CA=[(2,1,1),(2,2,1),(1,1,1)][(1,2,2),(2,2,3),(1,-1,3)]=[(5,5,10),(7,7,13),(4,3,8)]`
and `(CA)^(-1)=[(-17/5,2,1),(4/5,0,-1),(7/5,-1,0)]`
`implies (CA)^(-1) D=[(-17/5,2,1),(4/5,0,-1),(7/5,-1,0)][(10),(13),(9)]=[(1),(-1),(1)]`
`implies X=[(1),(-1),(1)]`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise (Single)|65 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.4|12 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

If A=[(1,2,3),(2,3,1)] and B=[(3,-1,3),(-1,0,2)], then find 2A-B.

If A'=[(-2,3),(1,3)] and B=[(-1,0),(1,2)], find [A+2B]'.

A=[[1,3,-12,2,-13,0,-1]] and B=[[-2,3,-1-1,2,-1-6,9,-4]]

If A+B=[(1,0),(1,1)] and A-2B=[(-1,1),(0,-1)] then A= (A) 1/3 [(1,1),(2,1)] (B) 1/3 [(2,1),(1,2)] (C) [(1,1),(2,1)] (D) none of these

IF A = [{:( -2,3,-1),( -1,2,-1),( -6,9,-4) :}] and B = [{:( 1,3,-1),( 2,2,-1),( 3,0,-1) :}] then

If A = [(1,2),(3,-2),(-1,0)]and B = [(1,3,2),(4,-1,3)] then find the order of AB.

If A=[[1, 2, 3], [-1, 1, 2], [1, 2, 4]], B=[[1], [2], [3]] and AX=B , then X=

If A=[(2,2),(-3,2)] and B=[(0,-1),(1,0)] then (B^-1A^-1)^-1= (A) [(2,-2),(2,3)] (B) [(3,-2),(2,3)] (C) 1/10 [ (2,2),(-2,3)] (D) 1/10 [(3,-2),(-2,2)]

CENGAGE-MATRICES-Exercise 13.5
  1. By the method of matrix inversion, solve the system. [(1,1,1),(2,5,7...

    Text Solution

    |

  2. Let A=[[2,0,7] , [0,1,0], [1,-2,1]] and B=[[-x,14x,7x] , [0,1,0] , [x,...

    Text Solution

    |

  3. Find A^(-1) if A=|(0,1,1),(1,0,1),(1,1,0)| and show that A^(-1)=(A^(2)...

    Text Solution

    |

  4. For the matrix A=[3 1 7 5] , find x and y so that A^2+x I=y Adot

    Text Solution

    |

  5. If A^(3)=O, then prove that (I-A)^(-1) =I+A+A^(2).

    Text Solution

    |

  6. If A=[[cos alpha, -sin alpha] , [sin alpha, cos alpha]], B=[[cos2beta,...

    Text Solution

    |

  7. If A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1,1),(2,2,1),(1,1,1)], D=[(10),...

    Text Solution

    |

  8. If A is a 2xx2 matrix such that A^(2)-4A+3I=O, then prove that (A+3I)^...

    Text Solution

    |

  9. For two unimobular complex numbers z(1) and z(2), find [(bar(z)(1),-z(...

    Text Solution

    |

  10. Prove that inverse of a skew-symmetric matrix (if it exists) is skew-s...

    Text Solution

    |

  11. If square matrix a is orthogonal, then prove that its inverse is also ...

    Text Solution

    |

  12. If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is...

    Text Solution

    |

  13. Prove that ("adj. "A)^(-1)=("adj. "A^(-1)).

    Text Solution

    |

  14. Using elementary transformation, find the inverse of the matrix A=[(a,...

    Text Solution

    |

  15. Show that the two matrices A, P^(-1) AP have the same characteristic r...

    Text Solution

    |

  16. Show that the characteristics roots of an idempotent matris are either...

    Text Solution

    |

  17. If alpha is a characteristic root of a nonsin-gular matrix, then prove...

    Text Solution

    |