Home
Class 12
MATHS
Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1)...

Let `A=((1,0,0),(2,1,0),(3,2,1))`. If `u_(1)` and `u_(2)` are column matrices such that `Au_(1)=((1),(0),(0))` and `Au_(2)=((0),(1),(0))`, then `u_(1)+u_(2)` is equal to :

A

`((-1),(-1),(0))`

B

`((1),(-1),(-1))`

C

`((-1),(1),(0))`

D

`((-1),(1),(-1))`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `u_(1) + u_(2) = ((x),(y),(z))`
Now, `Au_(1) + Au_(2) = ((1),(1),(0))`
`rArrA(u_(1) + u_(2)) = ((1),(1),(0))`
`rArr ((1,0,0),(2,1,0),(3,2,1)) ((x),(y),(z)) = ((1),(1),(0))`
`rArr ((x),(2x+y),(3x+2y+z)) = ((1),(1),(0))`
`therefore x = 1, 2x + y =1`
and ` 3x + 2y +=0`
`rArr x=1, y=-1, z=-1` Hence, `u_(1) + u_(2) = ((1),(-1),(1))`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|14 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

If A= ((1,0,0),(2,1,0),(3,2,1)), U_(1), U_(2), and U_(3) are column matrices satisfying AU_(1) =((1),(0),(0)), AU_(2) = ((2),(3),(0))and AU_(3) = ((2),(3),(1)) and U is 3xx3 matrix when columns are U_(1), U_(2), U_(3) then answer the following questions The value of [3 2 0] I((3),(2),(0)) is

If A=[{:(0,1),(1,0):}] then A^(2) is equal to

If A = [(1,0),(1/2,1)] , then A^100 is equal to

Let {:A=[(1,0,0),(2,1,0),(3,2,1)]:}and U_1,U_2,U_3 be column matrices satisfying {:AU_1=[(1),(0),(0)],AU_2=[(2),(3),(6)],AU_3=[(2),(3),(1)]:} .If U is 3xx3 matrix whose columns are U_1,U_2,U_3," then "absU=

Let A = [(1,0,0), (2,1,0), (3,2,1)], and U_1, U_2 and U_3 are columns of a 3 xx 3 matrix U . If column matrices U_1, U_2 and U_3 satisfy AU_1 = [(1),(0),(0)], AU_2 = [(2),(3),(0)], AU_3 = [(2),(3),(1)] then the sum of the elements of the matrix U^(-1) is

A = [ (0,0,1),(0,1,0),(1,0,0)] , verify that A^(2) = I

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three column matrices satisfying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). The ratio of the trace of the matrix B to the matrix C, is

Let A=[(1,1,1),(0,1,1),(0,0,1)] prove that by induction that A^n=[(1,n,n(n+1)/2),(0,1,n),(0,0,1)] for all n in N .

ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

    Text Solution

    |

  2. Let A and B two symmetric matrices of order 3. Statement 1 : A(BA) a...

    Text Solution

    |

  3. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2^(...

    Text Solution

    |

  4. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

    Text Solution

    |

  5. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

    Text Solution

    |

  6. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

    Text Solution

    |

  7. Let P and Q be 3xx3 matrices P ne Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2)P,...

    Text Solution

    |

  8. IF P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of 3xx3 matrix A and...

    Text Solution

    |

  9. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

    Text Solution

    |

  10. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

    Text Solution

    |

  11. If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A...

    Text Solution

    |

  12. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

    Text Solution

    |

  13. Let M and N be two 3xx3 matrices such that MN=NM. Further, if M ne N^(...

    Text Solution

    |

  14. If A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisying the equation A A...

    Text Solution

    |

  15. Let X \ a n d \ Y be two arbitrary, 3xx3 , non-zero, skew-symmetric ma...

    Text Solution

    |

  16. If A=[(5a,-b),(3,2)] and A adj A=A A^(T), then 5a+b is equal to

    Text Solution

    |

  17. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

    Text Solution

    |

  18. Let z=(-1+sqrt(3)i)/(2), where i=sqrt(-1), and r, s in {1, 2, 3}. Let ...

    Text Solution

    |

  19. Let P=[(1,0,0),(3,1,0),(9,3,1)] and Q = [q(ij)] be two 3xx3 matrices s...

    Text Solution

    |

  20. If A=[(2,-3),(-4,1)], then adj (3A^(2)+12 A) is equal to

    Text Solution

    |