I have a question where I have a matrix $$A=\begin{bmatrix}2&-1\\-1&1\end{bmatrix}$$ and I need to find two examples of a non-zero matrix $X$ such that $AX = XA$. My first matrix is \begin{bmatrix}1&0\\0&1\end{bmatrix} the identity matrix but I cant think of another one. Any ideas?
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2I'm confused. is $A$ given or not given? – Siong Thye Goh Nov 15 '17 at 23:15
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Do you mean $AB = BA$? Your question as it stands doesn't really make sense to me. – David Reed Nov 15 '17 at 23:17
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How about $B = \begin{bmatrix} -1 & 1\1& 0 \end{bmatrix}$ then $BA = AB$ – Doug M Nov 15 '17 at 23:18
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I think the OP means $A$ is given, $X$ and $B$ are unknown. – Landuros Nov 15 '17 at 23:21
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same question yesterday https://math.stackexchange.com/questions/2520448/give-two-examples-of-a-non-zero-matrix-textbfa-such-that-textbfax-te – Will Jagy Nov 15 '17 at 23:50
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How about $B=A=X$ then $AB = A^2 = BA$?
gt6989b
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probably was really this: https://math.stackexchange.com/questions/2520448/give-two-examples-of-a-non-zero-matrix-textbfa-such-that-textbfax-te – Will Jagy Nov 15 '17 at 23:51
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So we have $$A = \left[ \begin{array}{c c} 2 & -1 \\ -1 & 1 \end{array} \right]$$ Some simple answers include first taking $$X = \left[ \begin{array}{c c} 1 & 0 \\ 0 & 0 \end{array} \right]$$ Which gives $$AX = \left[ \begin{array}{c c} 2 & 0 \\ -1 & 0 \end{array} \right]$$ It's not too hard to guess and check to find $$B = \left[ \begin{array}{c c} 2 & 2 \\ -1 & -1 \end{array} \right]$$ does the trick.
AlkaKadri
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probably was really this: https://math.stackexchange.com/questions/2520448/give-two-examples-of-a-non-zero-matrix-textbfa-such-that-textbfax-t – Will Jagy Nov 15 '17 at 23:57