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Let {:A=[(1,0,0),(2,1,0),(3,2,1)]:}and U...

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=`

A

3

B

-3

C

`3//2`

D

2

Text Solution

Verified by Experts

The correct Answer is:
A
Let `U_(1)` be `((x),(y),(z)) " so that" ((1,0,0),(2,1,0),(3,2,1))((x),(y),(z)) =((1),(0),(0)) `
`rArr((x),(y),(z)) =((1),(-2),(1)) `
Similarly, `U_(2)=((2),(-1),(-4)),U_(3) =((2),(-2),(-3)) `
Hence, `U= ((1,2,2),(-2,-1,-1),(1,-4,-3))`
`therefore abs(U)=3`
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