Thread: Underlined letter in matrix notion

Originally Posted by DangerousDave

In the context of the equation

Ax = B

where A and B are matrices and the letter x is underlined, what does the latter represent? A column vector? I have to 'solve' by using the inverse of A multiplied by B, but I'm just wondering if I should produce a colum vector or some other kind of 'solution'.

Cheers

hey

for 'x' part of question:

basically 'x' is a common multipling matrix,

The constraints on x are as follows:

if A and B are 2x2 matrices, then x must be a 2x2 matrix
if A and B are 3x3 matrices, then x must be a 3x3 matrix
.
.
if A and B are nxn matrices, then x must be a nxn matrix

and obviously the matrix of B = the matrix of A* the matrix of x

for solving:

Normally in these problem they will want you to calculate the x-value

to do this you treat like you would any equation and make the equation into the form x=...
if you multiply by the invere of A on both sides you get:
(Ile use 'AI' to represent the inverse of A)

A*(AI)*x=B*(AI)

as A*(AI)=1, the equation becomes:

x=B*(AI)

and hence you can have/can work out the value of x
if theyve given you the values of B and A, you should work out the B*AI matrix components and write in terms of x

so (if x was a 3 x 3 matrix for example) wrtie as:

x =
[ a b c
d e f
g h i ]

otherwise writing it like 'x=B*(AI)' should be fine

hope this helps