Matrix equation

hoang1881

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Sep 26, 2020
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Hello everyone,
I need help with solving this matrix equation and am looking for help from you guys. :) thanks in advance. No need to mind the strange word "где" in the screenshot. it just indicates what matrices A and B look like.
MA TRẬN.jpg
 

tkhunny

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What "A and B look like" or what A and B ARE?

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

Jomo

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I am happy that you came back to find some help from this forum. I am anxious to help you so please reply stating what type of help you need and please show the work which you have done so far on this problem.
 

topsquark

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What "A and B look like" or what A and B ARE?

Have you considered solving for X in a standard, algebra sense?
One starting point:
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
 

Harry_the_cat

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

hoang1881

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Sep 26, 2020
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I assume that you are saying 2 - A here is 2E -A?
 

Jomo

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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.
 
Last edited:

topsquark

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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.
But you were just sent there. Shouldn't someone come in and sterilize it first?

-Dan
 

Jomo

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But you were just sent there. Shouldn't someone come in and sterilize it first?

-Dan
The rule is and has always that the next person sent to the corner has to clean it.
 

Harry_the_cat

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

Jomo

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