# Matrix equation

#### hoang1881

##### New member
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.

#### tkhunny

##### Moderator
Staff member
What "A and B look like" or what A and B ARE?

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

#### Jomo

##### Elite Member
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

##### Full Member
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

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

#### hoang1881

##### New member
I assume that you are saying 2 - A here is 2E -A?

#### Jomo

##### Elite Member
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.

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#### topsquark

##### Full Member
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

##### Elite Member
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

##### Senior Member
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

##### Elite Member
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.