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If A={:[(2,1),(0,3)]:}andf(x)=x^(2)-4x+3...

If `A={:[(2,1),(0,3)]:}andf(x)=x^(2)-4x+3`, then find f(A).

A

`{:[(-1,1),(0,0)]:}`

B

`{:[(0,0),(1,-1)]:}`

C

`{:[(0,1),(2,3)]:}`

D

`{:[(0,0),(1,2)]:}`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `A={:[(2,1),(0,3)]:}`
`f(x)=x^(2)-4x+3`
`f(A)=A^(2)-4A+3I`
`A^(2)={:[(2,1),(0,3)]:}{:[(2,1),(0,3)]:}`
`{:[(4+0,2+3),(0+0,0+9)]:}`
`{:[(4,5),(0,9)]:}`
`4A={:[(8,4),(0,12)]:}`
`3I={:[(3,0),(0,3)]:}`
`A^(2)-4A+3I={:[(4-8+3,5-4+0),(0-0+0,9-12+3)]:}`
`={:[(-1,1),(0,0)]:}`.
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