Home
Class 12
MATHS
If A=[{:(1,5),(7,12):}] and B=[{:(9,1),(...

If `A=[{:(1,5),(7,12):}]` and `B=[{:(9,1),( 7,8):}]` then find a matrix C such that `3A+5B+2C` is a null matrix.

Text Solution

Verified by Experts

The correct Answer is:
`[(-24,-10),(-28,-38)]`
We have, `A=[(1,5),(7,12)]` and `B=[(9,1),(7,8)]`
Let `C=[(a,b),(c,d)]`
`:. 3A+5B+2C=O`
`implies [(3,15),(21,36)]+[(45,5),(35,40)]+[(2a,2b),(2c,2d)]=[(0,0),(0,0)]`
`implies [(48+2a,20+2b),(56+2c,76+2d)]=[(0,0),(0,0)]`
So, we have
`2a+48=0implies a=-24`,
`20+2b=0implies b=-10`,
`56+2c=0 implies c=-28` ,
and `76+2d=0 implies d=-38`.
`:. C=[(-24,-10),(-28,-38)]`
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If A=[(8,0),(4,-2),(3,6)] and B=[(2,-2),(4,2),(-5,1)] , then find the matrix X, such that 2A+3X=5B .

If A-2B ={:[(1,5),(3,7)]and 2A-3B = {:[(-2,5),(0,7)]:} then matrix B is equal to__

If A = [(4,1),(7,2)] find a matrix B such that AB = I where I is the unit matrix of order 2.

Let A=[(2,-1),(3,4)], B=[(5,2),(7,4)], C=[(2,5),(3,8)] . Find a matrix D such that CD-AB=O .

A=({:(8,0),(4,-2):})" and "B = ({:(2,-2),(-5,1):}) , find another matrix X where 2A+3X=5B.

IF A={1,2,3,4,5} and U={0,1,2,3,4,5,6,7,8,9}, then find A^c .

If A = [[1,2],[3,-5]] and B=[[1,0],[0,2]] and X is a matrix such that A=BX , then X=

If A={:((1,-3,4,2),(0,5,-2,3))and B=((-5,0,6,4),(7,8,-2,5)), find a matrix X of order 2xx4 such that 3A-2X=B.

If 2X+[(1,2),(3,4)]=[(3,8),(7,2)] , then the matrix X is equal to -

If A= [[3,-1],[1,2]],B=[[3],[1]],C=[[1],[-2]] find the matrix X such that AX = 3B+2C.

CENGAGE PUBLICATION-MATRICES-All Questions
  1. If matric A is skew-symmetric matric of odd order, then show that tr. ...

    Text Solution

    |

  2. Solve for x and y , x[{:(2),(1):}]+y[{:(3),(5):}]+[{:(-8),(-11):}]=0.

    Text Solution

    |

  3. If A=[{:(1,5),(7,12):}] and B=[{:(9,1),( 7,8):}] then find a matrix C ...

    Text Solution

    |

  4. Solve the following equations for X and Y : 2X-Y=[(3,-3,0),(3,3,2)],...

    Text Solution

    |

  5. If A=[(1,2,3),(2,1,2),(2,2,3)]B=[(1,2,2),(-2,-1,-2),(2,2,3)] and C=[(-...

    Text Solution

    |

  6. If A=[(3,-2),(4,-1)], then find all the possible values of lambda such...

    Text Solution

    |

  7. If matrix A=[(0,1,-1),(4,-3,4),(3,-3,4)]=B+C, where B is symmetric mat...

    Text Solution

    |

  8. Consider the matrices A=[(4,6,-1),(3,0,2),(1,-2,5)], B=[(2,4),(0,1),...

    Text Solution

    |

  9. Let A=B B^(T)+C C^(T), where B=[(cos theta),(sin theta)], C=[(sin thet...

    Text Solution

    |

  10. if A=[[i,0] , [0,i]] where i=sqrt(-1) and x in N then A^(4x) equals to...

    Text Solution

    |

  11. If A = [[1,2],[3,-5]] and B=[[1,0],[0,2]] and X is a matrix such that ...

    Text Solution

    |

  12. Find the matrix X so that X[1 2 3 4 5 6]=[-7-8-9""""""2""""""4""""6]

    Text Solution

    |

  13. If A=[[costheta,sintheta],[-sintheta,costheta]],then Lim(ntooo)1/nA^n ...

    Text Solution

    |

  14. A=[(3,a,-1),(2,5,c),(b,8,2)] is symmetric and B=[(d,3,a),(b-a,e,-2b-c)...

    Text Solution

    |

  15. If A and B are matrices of the same order, then A B^T-B A^T is a (a)...

    Text Solution

    |

  16. If A and B are square matrices such that AB = BA then prove that A^(3)...

    Text Solution

    |

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

    Text Solution

    |

  18. If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , t...

    Text Solution

    |

  19. Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0.

    Text Solution

    |

  20. Let A be a matrix of order 3, such that A^(T)A=I. Then find the value ...

    Text Solution

    |