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=`

Options

A. 3
B. -3
C. `3//2`
D. 2

Answer

A

Explanation

Let `{:U_1[(a),(b),(c)],U_2[(p),(q),(r)],andU_3[(x),(y),(z)]:}` Then
`{:AU_1[(1),(0),(0)]rArr[(a),(2a+b),(3a+2b+c)]=[(1),(0),(0)]rArra=1,b=-2, c=1:}`
`{:AU_2[(2),(3),(0)]rArr[(p),(2p+q),(3p+2q+r)]=[(2),(3),(0)]rArrp=2,q=-1,r=4:}`
and,
`{:AU_2[(2),(3),(1)]rArr[(x),(2x+y),(3x+2y+z)]=[(2),(3),(1)]rArrx=2,y=-1,z=-3:}`
`:. U{:abs((U_1,U_2,U_3))=[(1,2,2),(-2,-1,-1),(1,-4,-3)]:}`
`rArr absU={:abs((1,2,2),(-2,-1,-1),(1,-4,-3)) =abs((1,2,0),(-2,-1,0),(1,-4,1)):}" Applying " C_3 to C_3-C_2`
`rArr absU=3`