- Thread starter hoang1881
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- Aug 27, 2012

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- 959

One starting point:What "A and B look like" or what A and B ARE?

Have you considered solving for X in a standard, algebra sense?

2X + 8A = XA - B

Let

\(\displaystyle X = \left [ \begin{matrix} w & x \\ y & z \end{matrix} \right ]\)

\(\displaystyle A = \left [ \begin{matrix} 2 & -3 \\ 1 & -4 \end{matrix} \right ]\)

\(\displaystyle B = \left [ \begin{matrix} \text{-9} & 0 \\ \text{-4} & 11 \end{matrix} \right ]\)

So

\(\displaystyle 2 \left [ \begin{matrix} w & x \\ y & z \end{matrix} \right ] + 8 \left [ \begin{matrix} 2 & -3 \\ 1 & -4 \end{matrix} \right ] = \left [ \begin{matrix} w & x \\ y & z \end{matrix} \right ] \cdot \left [ \begin{matrix} 2 & -3 \\ 1 & -4 \end{matrix} \right ] - \left [ \begin{matrix} \text{-9} & 0 \\ \text{-4} & 11 \end{matrix} \right ]\)

Multiply it out. 4 equations and 4 unknowns.

Another starting point:

2X + 8A = XA - B

2X - XA = -8A - B

We can change the order of 2 and X in the first term on the RHS:

X2 - XA = -(8A + B)

X(2 - A) = -(8A + B)

\(\displaystyle X = -(8A + B) \cdot (2 - A)^{-1}\)

Of course, this is useless if you can't find \(\displaystyle (2 - A)^{-1}\). But \(\displaystyle Det(2 - A) \neq 0\) so the inverse does exist.

-Dan

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Hey Dan,

Shouldn't 2-A be 2I-A ? where I is the 2x2 identity matrix?

Shouldn't 2-A be 2I-A ? where I is the 2x2 identity matrix?

- Joined
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What's E?I assume that you are saying 2 - A here is 2E -A?

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- Joined
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But you were just sent there. Shouldn't someone come in and sterilize it first?Yes, I have to say the same comment: Shouldn't 2-A be 2I-A ? That error certainly requires some serious corner time for you.

-Dan

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- Dec 30, 2014

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The rule is and has always that the next person sent to the corner has to clean it.But you were just sent there. Shouldn't someone come in and sterilize it first?

-Dan

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- Mar 16, 2016

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But that's not COVID-safe! The rules have changed!The rule is and has always that the next person sent to the corner has to clean it.

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I never got the message regarding the change. Besides, going to the corner is for punishment not for safety.But that's not COVID-safe! The rules have changed!