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Mathematics
Mathematics
Problem
Consider the matrix
A
=
(
k
1
2
k
)
A=\begin{pmatrix}k & 1\\2 & k\end{pmatrix}
A
=
(
k
2
1
k
)
. The
(
1
,
2
)
(1,2)
(
1
,
2
)
element of
A
−
1
A^{-1}
A
−
1
equals
−
1
k
2
−
2
\dfrac{-1}{k^{2}-2}
k
2
−
2
−
1
. For which value(s) of
k
k
k
is this statement true? a)
k
=
±
2
k=\pm\sqrt{2}
k
=
±
2
only b)
k
=
±
3
k=\pm\sqrt{3}
k
=
±
3
c) All real
k
k
k
except
k
=
±
2
k=\pm\sqrt{2}
k
=
±
2
d) All real
k
k
k
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