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2013 VTRMC
Problem 6
Problem 6
Part of
2013 VTRMC
Problems
(1)
matrix inverse problem
Source: VTRMC 2013 P6
5/12/2021
Let \begin{align*}X&=\begin{pmatrix}7&8&9\\8&-9&-7\\-7&-7&9\end{pmatrix}\\Y&=\begin{pmatrix}9&8&-9\\8&-7&7\\7&9&8\end{pmatrix}.\end{align*}Let
A
=
Y
−
1
X
A=Y^{-1}X
A
=
Y
−
1
X
and let
B
B
B
be the inverse of
X
−
1
+
A
−
1
X^{-1}+A^{-1}
X
−
1
+
A
−
1
. Find a matrix
M
M
M
such that
M
2
=
X
Y
−
B
Y
M^2=XY-BY
M
2
=
X
Y
−
B
Y
(you may assume that
A
A
A
and
X
−
1
+
A
−
1
X^{-1}+A^{-1}
X
−
1
+
A
−
1
are invertible).
linear algebra
matrix