3
4
[24
45. (a) Given A:
and B =
; find the matrix X such that AX = B.
4
-3
7
Answers
Answered by
1
Answer:
I have a problem of the form XAX⊤=B, where A and B are symmetric matrices and X need not be symmetric. I'd like to solve for X, e.g. by expressing the problem as Cvec(X)=D (where vec is the vectorization operation) and solving by least squares. I'm looking for ways to express the problem in a solvable way. I'm familiar with the vec trick but that just seems to make things worse in this case.
Answered by
1
AX=B,
∴[
1
−1
2
3
]X=[
0
2
1
4
]
By R
2
+R
1
we get
[
1
0
2
5
]=[
0
2
1
5
]
By (
5
1
)R
2
we get
[
1
0
2
1
]X=
⎣
⎢
⎡
0
5
2
1
1
⎦
⎥
⎤
By R
1
−2R
2
we get
[
1
0
0
1
]X=
⎣
⎢
⎢
⎡
−
5
4
5
2
−1
1
⎦
⎥
⎥
⎤
∴X=
⎣
⎢
⎢
⎡
−
5
4
5
2
−1
1
⎦
⎥
⎥
⎤
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