Solving Matrix: AX + B = CA | X + A'B = C

[TranscendArcu]

Homework Statement

The Attempt at a Solution

I think I'm oversimplifying this problem. Why can't I just write:

AX + B =CA
X + A'B = C
X = C - A'B

?

 

[lanedance]

does your notation mean A' = A^{-1}?

... if so, you can't do what you propse because matrix multiplication does not necesarrily commute. ionce you fix that, you're not far off the answer

 

[TranscendArcu]

Yes, that's what I intended my notation to convey.

Do I have to write:

AX + B = CA
AX = CA - B
A'(AX) = A'(CA - B)
IX = A'CA - A'B
X = A'CA - A'B

?

 

[lanedance]

that looks better

 

[Mark44]

AX + B =CA
X + A'B = C
X = C - A'B

does your notation mean A' = A^{-1}?

The notation A' is sometimes used to mean the transpose of matrix A. For inverses, I don't think I've ever seen ' used to indicate the inverse.

It's just as easy to write an exponent of -1 as an exponent of 2 or 3, and the intent is much clearer.

At the bottom of the input pane, click the Go Advanced button. This opens a menu of icons at the top of the input pane. The X² button let's you write exponents, which it does by inserting [ sup ] and [ /sup ] tags (without the spaces).

You can also do this manually, like so: A[noparse]^-1[/noparse]. I have inserted some other tags so that you could see the sup tags. Without those other tags, what I wrote renders like this: A^-1.