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A is a 2xx2 matrix such that A[[1],[-1]]...

`A` is a `2xx2` matrix such that `A[[1],[-1]]=[[-1],[ 2]] and A^2[[1],[-1]]=[[1],[ 0]]dot` The sum of the elements of `A` is a.`-1` b. 0 c. 2 d. 5

A

`-1`

B

0

C

2

D

5

Text Solution

Verified by Experts

The correct Answer is:
D
`A[(1),(-1)]=[(-1),(2)]` (1)
`A^(2)[(1),(-1)]=[(1),(0)]` (2)
Let a be given by `A=[(a,b),(c,d)]`. The first equation gives
`a-b=-1` (3)
`c-d=2` (4)
For the second equation,
`A^(2)[(1),(-1)]=A(A[(1),(-1)])=A([(-1),(2)])=[(1),(0)]`
This gives
`-a+2b=1` (5)
`-c+2d=0` (6)
Eqs, (3) + (5) gives `b=0` and `a=-1`
Eqs. (4) + (6) gives `d=2` and `c=4`
So the sum `a+b+c+d=5`.
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