Home
Class 12
MATHS
Let A=[{:(3," "4),(-2," "0),(7,-5):}]" a...

Let `A=[{:(3," "4),(-2," "0),(7,-5):}]" and "B=[{:(2,-3),(5," "6),(-1," "8):}].` Verify that `(A+B)'=A'+B'.`

Text Solution

Verified by Experts

We have
`A+B=[{:(3," "4),(-2," "0),(7,-5):}]+[{:(2,-3),(5," "6),(-1," "8):}]`
`=[{:(3+2,4+(-3)),(-2+5," "0+6),(7+(-1),-5+8):}]=[{:(5,1),(3,6),(6,3):}].`
`:." "(A+B)'=[{:(5,1),(3,6),(6,3):}]'=[{:(5,3,6),(1,6,3):}].`
Also, `A'=[{:(3," "4),(-2," "0),(7,-5):}]'=[{:(3,-2," "7),(4," "0,-5):}].`
And, `B'=[{:(2,-3),(5,6),(-1,8):}]'=[{:(2,5,-1),(-3,6," "8):}].`
`:." "(A'+B')=[{:(3,-2," "7),(4," "0,-5):}]+[{:(2,5,-1),(-3,6," "8):}]`
`=[{:(3+2,-2+5," "7+(-1)),(4+(-3)," "0+6," "-5+8):}]=[{:(5,3,6),(1,6,3):}].`
Hence, `(A+B)'=A'+B'.`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    RS AGGARWAL|Exercise Exercise 5A|9 Videos

  • MATRICES

    RS AGGARWAL|Exercise Exercise 5B|16 Videos

  • LINEAR PROGRAMMING

    RS AGGARWAL|Exercise SECTION D|6 Videos

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise Objective Questions Ii|56 Videos

Similar Questions

Explore conceptually related problems

Let A=[{:(" "2,3,5),(-1,0,4):}]" and "B=[{:(4,-2,3),(2," "6,-1):}]. Verify that A+B=B+A.

Let A=[{:(1,-2),(5," "4),(3," "0):}],B=[{:(" "3," "1),(" "0," "2),(-3," "5):}]" and "C=[{:(" "4," "3),(-2," "2),(" "1," "6):}]. Verify that (A+B)+C=A+(B+C).

If A=[{:(" "2,-3,5),(-1," "0,3):}]" and "B=[{:(3,2,-2),(4,-3," "1):}] , verify that (A+B)=(B+A).

If A=[{:(3," "5),(-2," "0),(6,-1):}],B=[{:(-1,-3),(4," "2),(-2," "3):}]" and "C=[{:(0," "2),(3,-4),(1," "6):}], Verify that (A+B)+C=A+(B+C).

If A= [{:(,-2),(,4),(,5):}] , B=(1,3-6) verify that (AB)'=B'A'

If A=[{:(3,2),(1,0):}],B=[{:(1,-2,5),(0,7,3):}]" and "C=[{:(8,1,-6),(2,-5,0):}] , verify that A(B+C)=(AB+AC).

If A=[(3),(-4),(5)],B=["6 1 -1"] , verify that : (AB)'=B'A' .

Find matrices A and B, if A+B=[{:(1,0," "2),(5,4,-6),(7,3," "8):}]" and "A-B=[{:(-5,-4,8),(11," "2,0),(-1," "7,4):}].

If A=[{:(-3),(" "5),(" "2):}] and B=[1" "6" "-4] then verify that (AB)'=B'A'.

Let A=[{:(0,1,-2),(5,-1,-4):}],B=[{:(1,-3,-1),(0,-2," "5):}]" and "C=[{:(2,-5,1),(-4," "0,6):}]. Compute 5A-3B+4C.

RS AGGARWAL-MATRICES-Exercise 5F
  1. Let A=[{:(3," "4),(-2," "0),(7,-5):}]" and "B=[{:(2,-3),(5," "6),(-1,"...

    Text Solution

    |

  2. Construct a 2xx3 matrix whose elements are given by a(ij)=(1)/(2)(i-...

    Text Solution

    |

  3. Construct a 2xx3 matrix whose elements are given by a(ij)=(1)/(2)|-3...

    Text Solution

    |

  4. If [{:(x+2y,-y),(3x,4):}]=[{:(-4,3),(6,4):}], find the values of x and...

    Text Solution

    |

  5. Find the values of x and y, if 2[{:(1,3),(0,x):}]+[{:(y,0),(1,2) :}]...

    Text Solution

    |

  6. If x.[{:(2),(3):}]+y.[{:(-1),(1):}]=[{:(10),(5):}], find the values of...

    Text Solution

    |

  7. If [{:(x,3x-y),(2x+z,3y-w):}]=[{:(3,2),(4,7):}], find the values of w...

    Text Solution

    |

  8. If [{:(x,6),(-1,2w):}]+[{:(" "4,x+y),(z+w," "3):}]=3[{:(x,y),(z,w):}],...

    Text Solution

    |

  9. If A=" diag "(3" "-2" "5)" and "B=" diag "(1" "3" "-4)," find "(A+B).

    Text Solution

    |

  10. Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sint...

    Text Solution

    |

  11. If A=[{:(1,-5),(-3," "2),(4,-2):}]" and "B=[{:(3," "1),(2,-1),(-2," "3...

    Text Solution

    |

  12. If A=[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}], then find the lea...

    Text Solution

    |

  13. Find the values of x and y for which [{:(2,-3),(1," "1):}][{:(x),(y)...

    Text Solution

    |

  14. Find the values of x and y for which [{:(x,y),(3y,x):}][{:(1),(2):}]...

    Text Solution

    |

  15. If A=[{:(4,5),(1,8):}], show that (A+A') is symmetric.

    Text Solution

    |

  16. If A=[{:(2,3),(4,5):}], show that (A-A') is skew-symmetric.

    Text Solution

    |

  17. If A=[{:(2,-3),(4," "5):}]" and "B=[{:(-1,2),(0,3):}], find a matrix X...

    Text Solution

    |

  18. If A=[{:(4,2),(1,3):}]" and "B=[{:(-2,1),(3,2):}], find a matrix X suc...

    Text Solution

    |

  19. If (i) A=[cosalphasinalpha-sinalphacosalpha] , then verify that Aprime...

    Text Solution

    |

  20. If A and B are two symmetric matrix of same order, then show that (AB-...

    Text Solution

    |

  21. If f(x)=x^2-4x+1 then find f(A) when A=[[2,3] , [1,2]]

    Text Solution

    |