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Let A = [(1,0,0), (2,1,0), (3,2,1)], and...

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

-1

B

0

C

1

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
`because " Adj"U = ((-1,-2,0),(-7,-5,-3),(9,-6,3))`
`therefore U^(-1) =("Adj"U)/abs(U) = ("Adj"U)/3`
`rArr` sum of the elements of
`U^(1) = 1/3(-1-2+0-7-5-3+9+6+3)=0`
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ARIHANT MATHS ENGLISH-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If A^(2)-A+I=O, then A^(-1) is equal to

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  2. Let {:A=[(1,0,0),(2,1,0),(3,2,1)]:}and U1,U2,U3 be column matrices sat...

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  3. Let A = [(1,0,0), (2,1,0), (3,2,1)], and U1, U2 and U3 are columns of ...

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  4. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

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  5. Let A=[{:(1,2),(3,4):}]and B = [{:(a,0),(0,b):}] where a, b are natura...

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  6. If A and B are square matrices of size nxxn such that A^2-B^2 = (A-B)(...

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  7. Let A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]] . If |A^2|...

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  8. Let A and B be 3xx3 matrtices of real numbers, where A is symmetric, "...

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  9. Let A be a square matrix all of whose entries are integers. Then wh...

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  10. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identi...

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  11. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  12. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  13. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  14. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

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  15. The number of 3xx3 matrices a whose entries are either 0 or 1 and for ...

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  16. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  17. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  18. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  19. Let K be a positive real number and A=[(2k-1,2sqrt(k),2sqrt(k)),(2sqrt...

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  20. The number of 3 x 3 non-singular matrices, with four entries as 1 and ...

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