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I would really appreciate any help on this problem. 

Let \(\mathbf{A}\) and \(\mathbf{B}\) be matrices, and let \(x\) and \(y \) be vectors such that neither is a scalar multiple of the other satisfying
 

\(\mathbf{A} \mathbf{x} = \mathbf{y}, \mathbf{A} \mathbf{y} = \mathbf{x} + 2\mathbf{y}\)

 

and

 

\(\mathbf{B} \mathbf{x} = \mathbf{x} + \mathbf{y}, \mathbf{B} \mathbf{y} = 2\mathbf{y}.\)

 

Then there exist scalars \(a, b, c, d\) such that

 

\(\begin{align*} (\mathbf{A}\mathbf{B})\mathbf{x} = a \mathbf{x} + b\mathbf{y},\\ (\mathbf{B}\mathbf{A})\mathbf{x} = c \mathbf{x} + d\mathbf{y}. \end{align*}\)

 

 

Enter \(a, b, c, d\) in that order

 

Thank for any help in advance 

 Jul 21, 2022
 #1
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(a,b,c,d) = (5,6,2,4)

 Jul 22, 2022
 #2
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Hello, Thank you for the help, 

 

But that answer seems to be wrong. 

 Jul 22, 2022

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