Home
Class 12
MATHS
if A=[{:(1,2,-3),(5,0,2),(1,-1,1):}],B=[...

`if A=[{:(1,2,-3),(5,0,2),(1,-1,1):}],B=[{:(3,-1,2),(4,2,5),(2,0,3):}]and c=[{:(4,1,2),(0,3,2),(1,-2,3):}],` then compure (A+B) and (B-C), Also , verify that A+(B-C)=(A+B)-C.`

Text Solution

Verified by Experts

The correct Answer is:
N/a
`A+B=[{:(1,2,-3),(5,0,2),(1,-1,1):}]+[{:(3,-1,2),(4,2,5),(2,0,3):}]`
`=[{:(4,1,-1),(9,2,7),(3,-1,4):}]`
`B-C[{:(3,-1,2),(4,2,5),(2,0,3):}]-[{:(4,1,2),(0,3,2),(1,-2,3):}]`
`=[{:(-1,-2,0),(4,-1,3),(1,2,0):}]`
`Now L.H.S=A+(B-C)`
`=[{:(1,2,-3),(5,0,2),(1,-1,1):}]+[{:(-1,-2,0),(4,-1,3),(1,2,0):}]=[{:(0,0,-3),(9,-1,5),(2,1,1):}]`
`R.H.S =(A+B)-C`
`=[{:(4,1,-1),(9,2,7),(3,-1,4):}]-[{:(4,1,2),(0,3,2),(1,-2,3):}]=[{:(0,0,-3),(9,-1,5),(2,1,1):}]`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    NAGEEN PRAKASHAN|Exercise Exercise 3.3|12 Videos

  • MATRICES

    NAGEEN PRAKASHAN|Exercise Exercise 3.4|18 Videos

  • MATRICES

    NAGEEN PRAKASHAN|Exercise Exercise 3.1|10 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|9 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

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=[(1,2,3),(-1,0,2),(1,-8,-1)],B=[(4,5,6),(-1,0,1),(2,1,2)],C=[(-1,-2,1),(-1,2,3),(-1,-2,2)] , find (i) 2B-3C (ii) A-2B+3C .

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).

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.

If A=[{:(" "1,-1," "2),(" "3," "2," "0),(-2," "0," "1):}],B=[{:(3,1),(0,2),(-2,5):}]" and "C=[{:(2,1,-3),(3,0,-1):} then verify that (AB)C=A(BC).

Let A=[(1,2),(2,1)],B=[(2,0),(1,3)] and C=[(1,1),(2,3)] . Calculate AC, BC and (A+B) C. Also, verify that (A+B)C=AC+BC.

Let A+B+C= [{:(,4,-1),(,0,1):}],4A+2B+C=[{:(,0,-1),(,-3,2):}]and 9A+3B+C=[{:(,0,2),(,2,1):}]"then find A"

If A=[1 2-3 5 0 2 1-1 1], B=[3-1 2 4 2 5 2 0 3] and C=[4 1 2 0 3 2 1-2 3] , then compute (A+B)" "a n d" "(B" "" "C) . Also, verify that A" "+" "(B" "" "C)" "=" "(A" "+" "B)" "" "C .

Given A=[(1,2,-3),(5,0,2),(1,-1,1)] and b=[(3,-1,2),(4,2,5),(2,0,3)] , find the matrix C such that A+C=B .

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

NAGEEN PRAKASHAN-MATRICES-Exercise 3.2
  1. compute the following : (i) [{:(a,b),(-b,a):}]+[{:(a,b),(b,a):}] (...

    Text Solution

    |

  2. compute the indicated products . (i) [{:(a,b),(-b,a):}][{:(a,-b),(b,...

    Text Solution

    |

  3. if A=[{:(1,2,-3),(5,0,2),(1,-1,1):}],B=[{:(3,-1,2),(4,2,5),(2,0,3):}]a...

    Text Solution

    |

  4. If A=[2/3 1 5/3 1/3 2/3 4/3 7/3 2 2/3] and B=[2/3 2/5 1 1/5 2/5 4/5 7/...

    Text Solution

    |

  5. Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+si...

    Text Solution

    |

  6. Find X and Y, if(i) X+Y=[7 0 2 5]and X-Y=[3 0 0 3](ii) 2X+3Y=[2 3 4 0]...

    Text Solution

    |

  7. Find X if Y=[3 2 1 4] and 2X+Y=[1 0-3 2] .

    Text Solution

    |

  8. Find X and Y,if 2[{:(1,3),(0,x):}]+[{:(y,0),(1,2):}]=[{:(5,6),(1,8...

    Text Solution

    |

  9. Solve the equation for x, y, z and t, if 2[x z y t]+3[1-1 0 2]=3[3 5 4...

    Text Solution

    |

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

    Text Solution

    |

  11. Given 3[x y z w]-[x6-1 2w]+[4x+y z+w3] , find the values of x, y, z an...

    Text Solution

    |

  12. If f(x) = [(cos x , - sinx,0),(sinx,cosx,0),(0,0,1)] then show f(x) . ...

    Text Solution

    |

  13. show that (i) [{:(5,-1),(6,7):}][{:(2,3),(3,4):}]ne[{:(2,3),(3,4):}]...

    Text Solution

    |

  14. If f(x)=x^2-5x+6. Find f(A),if A=[(2,0,1),(2,1,3),(1,-1,0)].

    Text Solution

    |

  15. If A=[1 0 2 0 2 1 2 0 3] , prove that A^3-6A^2+7A+2I=0

    Text Solution

    |

  16. If A A=[3-2 4-2]and I=[1 0 0 1], find k so that A^2=k A-2I.

    Text Solution

    |

  17. Let A=[0-tan(alpha//2)tan(alpha//2)0] and I be the identity matrix ...

    Text Solution

    |

  18. A trust fund has Rs. 30000 that must be invested in two different t...

    Text Solution

    |

  19. The bookshop of a particular school has 10 dozen chemistry books, 8...

    Text Solution

    |

  20. the restriction on n, k and p so that PY +Wywill be defined are :

    Text Solution

    |