Matrix equation

hoang1881

New member
Joined
Sep 26, 2020
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5
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
 
What "A and B look like" or what A and B ARE?

Have you considered solving for X in a standard, algebra sense?
 
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.
 
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
[math]X = \left [ \begin{matrix} w & x \\ y & z \end{matrix} \right ][/math]
[math]A = \left [ \begin{matrix} 2 & -3 \\ 1 & -4 \end{matrix} \right ][/math]
[math]B = \left [ \begin{matrix} \text{-9} & 0 \\ \text{-4} & 11 \end{matrix} \right ][/math]
So
[math]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 ][/math]
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)

[math]X = -(8A + B) \cdot (2 - A)^{-1}[/math]
Of course, this is useless if you can't find [math](2 - A)^{-1}[/math]. But [math]Det(2 - A) \neq 0[/math] so the inverse does exist.

-Dan
 
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:
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
 
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