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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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