The matrix has the same function to matrices as the number has to numbers.
If you multiply any number by one and you will get the same number back.
If you multiply any matrix by and you will get the same matrix back.
Nothing more to it!
I'm teaching myself matrices because it could prove useful in the future.
I'll just run through a few things I've done to check if I'm correct:
i'm confident in adding/subtracting and multiplying.
What I'm having trouble getting my mind around is identities, inverses and determinants for 2x2 matrices.
In my book it says that for matrices of a given dimension (2x2) a identity I exists...
What does this I mean?
Then after this it says
If
I have no idea in the world what this means. Could someone clarify it for me please =]
Thanks in advanced!
(Put the -1 in { } to get the whole thing as the exponent.)
If you multiply [tex]AA^{-1}= \left(\begin{array}{cc}3&2\\1&6\end{array}\right) \left(\begin{array}{cc}3&2\\1&6\end{array}\right)= \left(\begin{array}{cc}16 & 0 \\ 0 & 16\end{array}\right)[/quote]
The "1/16" in front gives the indentity matrix- the determinant of A is 16 and that is one over the determinant. In other words, "I" is like "1" in the real numbers and " is like 1/A.
There are a variety of different ways to find the inverse of a matrix (provided it has one- many matrices do not have inverses) and I don't know which your text gives.
My preference is: Write A and the identity matrix side by side. Use a series of "row operations" to reduce A to the indentity matrix while simultaneously applying those same row operations to the indentity matrix. When A has been reduced to the indentity matrix, the identity matrix will have been change to .