Solve for X in AXB=C: Matrices Question 4

[BilloRani2012]

Homework Statement

If:

A = l 1 -3 l , B = l -1 2 l C = l -12 -11 l
l 2 1 l l 3 1 l l -10 -1 l

Then, find X if AXB=C

Homework Equations

The Attempt at a Solution

I don't know how I would start this problem??

 

[Delphi51]

I think you would pick 4 variables, say t,u,v,w to represent the 4 elements in matrix X. Perform the multiplication and set the result equal to C. This should give you four ordinary equations, one for each element. Solve them for t,u,v,w.

 

[BilloRani2012]

When you say: Perform the multiplication and set the result equal to C. Do you mean multiply A&B?

 

[Delphi51]

"find X if AXB=C" means you multiply A by X, then the result by B.
Set that result equal to C.

 

[ehild]

It might be easier to find the inverse of both A and B and to multiply the matrix equation AXB=C with A^-1 from left and B^-1 from right to get X. (X=A^-1CB^-1)

ehild

 

[iRaid]

Don't you need the cross product and not multiplication?

 

[ehild]

X is not for "cross product" it is an unknown matrix you need to find.

ehild