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Question

A=100210321,U1,U2 and U3 are columns matrices satisfying AU1=100,AU2=230,AU3=231 and U is 3×3 matrix whose columns are U1,U2,U3 then answer the following question
The value of [320]U320 is

A
[5]
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B
[52]
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C
[4]
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D
[32]
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Solution

The correct option is A [5]
Let U1=(a b c)T
Then, we need to solve three simultaneous linear equations to get a,b,c
a=1
2a+b=0
3a+2b+c=0
On solving, we get a=1,b=2,c=1
So, U1=(1 2 1)T
Similarly solving for U2 and U3, we get,
U2=(2 1 4)T
U3=(2 1 3)T
U[3 2 0]T=[7 8 5]T

[3 2 0][7 8 5]T=[5]

So, Option (A)

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