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Multiple choice
The matrix
A
=
[
3
1
1
3
]
A = \begin{bmatrix}3 & 1 \\ 1 & 3\end{bmatrix}
A
=
[
3
1
1
3
]
has eigenvalues 4 and 2. For the function
f
(
x
)
=
x
f(x) = \sqrt{x}
f
(
x
)
=
x
, what is
T
r
(
f
(
A
)
)
=
4
+
2
\mathrm{Tr}(f(A)) = \sqrt{4} + \sqrt{2}
Tr
(
f
(
A
))
=
4
+
2
?
6
\sqrt{6}
6
≈ 2.449
6 (the trace of A)
2
+
2
2 + \sqrt{2}
2
+
2
≈ 3.414
8
\sqrt{8}
8
≈ 2.828
Check answer