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If A={:[(1,-4),(3,2)]:}andB={:[(6,-1),(3...

If `A={:[(1,-4),(3,2)]:}andB={:[(6,-1),(3,2)]:}`, then find the matrix C such that `C=AB+B^(2)`.

A

`{:[(37,25),(16,9)]:}`

B

`{:[(27,-17),(48,2)]:}`

C

`{:[(4,5),(17,16)]:}`

D

`{:[(3,-15),(6,18)]:}`

Text Solution

Verified by Experts

The correct Answer is:
B
`AB={:[(1,-4),(3,2)]:}={:[(6,-1),(3,2)]:}`
`={:[(-6,-9),(24,1)]:}`.
`B^(2)={:[(6,-1),(3,2)]:}={:[(6,-1),(3,2)]:}`
`={:[(36-3,-6-2),(18+6,-3+4)]:}`
`={:[(33,-8),(24,1)]:}`
`C=AB+B^(2)`
`={:[(-6+33,-9-8),(24+24,1+1)]:}`
`={:[(27,-17),(48,2)]:}`
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