Matrix equation, solve for X

[mpdancow]

Hi everybody! I need some help with this matrix equation:

A-XB=I

A and B are 2x2 matrices:

A=
6 1
-3 -8

B=
1 6
-1 5

I get this: -X=I*B(inverted)-A

Is this correct? Also, is -X different from X when it comes to matrices? Should I just see it as -1 times the matrix X, so then I would multiply all the numbers in the matrix with -1? I appreciate any help I can get with this!

 

[stapel]

I am assuming that the matrices are as follows:

A-XB=I

A and B are 2x2 matrices:

. . . . .\(\displaystyle A\, =\, \left[\, \begin{array}{rr}6&1\\-3&-8 \end{array}\,\right]\)

. . . . .\(\displaystyle B\, =\, \left[\, \begin{array}{rr}1&6\\-1&5 \end{array}\, \right]\)

If either of these is incorrect, kindly please provide corrections. Otherwise:

I get this: -X=I*B(inverted)-A

How did you obtain this? By what steps? For instance, you started with the initial equation:

. . . . .\(\displaystyle A\, -\, XB\, =\, I\)

You swapped the I and the XB (eliminating "minus" signs) to get:

. . . . .\(\displaystyle A\, -\, XB\, +\, XB\, -\, I\, =\, I\, -\, I\, +\, XB\)

. . . . .\(\displaystyle A\, -\, I\, =\, XB\)

Then you multiplied, on the right, by the inverse of B to get:

. . . . .\(\displaystyle \left(A\, -\, I\right)\, B^{-1}\, =\, XB\, B^{-1}\, =\, X\)

How did you get from here to your final result?

...is -X different from X when it comes to matrices?

Of course it is. Scalar multiplication by anything other than "1" is going to result in a new matrix, since all of the entries in the matrix will have been multiplied by that scalar value. Has your class not covered scalars yet?

Also, are you supposed to be solving for the actual matrix X, with its entries, etc? Or did the instructions (not included) say something else? Thank you!