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How do I add, subtract, multiply and divide matrices with different dimensions?

For adding and subtracting matricies, they MUST be the same dimension. When you have two equal dimension matricies, adding and subtracting is easy, you just add or subtract the two numbers in each position to get the answer in that position.

For multiplying matricies, there is another catch: the length of one must equal the width of the other. For example, you cannot (though you may think you can) multiply equal dimension matricies if they are not square. So, multiplying a 3x2 and another 3x2 matrix is impossible. You CAN multiply a 3x2 and a 2x3. You can also multiply a 7x2 by a 2x1. Just look at the middle two numbers, they are both 2's, so it's good. Even if you satisfy the dimension condition, multiplying it out is tricky. One thing that is hard to remember is that matrix multiplication is NOT communative ([A] does NOT equal [A]). In fact, most of the time it is possible to switch unless it is square. Take that 7x2 multiplied by that 2x1 matrix. You can't multiply the 2x1 by the 7x2. Once that's all figured out, then you must multiply each number in a position by all of the numbers in the same row on the other matrix. I have to saw, I looked for a good example, and wikipedia had a good one. Just ignore the summation, and go to the coefficient vector method: http://en.wikipedia.org/wiki/Matrix_multiplication

I'm afraid that division is just, if not more, complex than multiplication. If you have a TI-83 or TI-84, these things are all made easier, as you can create matricies and play with them. That is, if you know the rules.

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