CHAPTER 01.10: INTRODUCTION: Equal Matrices So let’s talk about when two matrices are
considered to be equal. So 2 matrices are considered to be equal- so two
matrices, so A and B are equal. So two things have
to be considered when you consider two matrices to be equal. If the size of A
and B are the same and AIJ is equal to BIJ for all I, J. So in layman’s terms
that means that, if the A matrix is M by N then B has to be M by N. They
don’t have to be square matrices but the number of rows in A has to be the
same as the rows in B. The number of columns in A has to be the same as the
number of columns in B. All of the elements have to be equal, as far as the
corresponding elements are concerned. So the I row
and J column has to be the same as I row and J column of B as well as in A. So let’s look at an example. So somebody says “Hey,
I got this A matrix here. 2, 3, 6, 7.” And then I have a B matrix here. What will
make this matrix to be same as this matrix? So the first thing we have to
realize is that is 2 row two columns. So B also has to have two rows and two
columns. So it all has to be the same. The same number of rows here and the
same number of rows here. The same number of columns here and the same number
of columns here. But each element has to be the same. So this is A 1 1, first row, first column, has to be the same as the
first row first column here. This has to be 2. Then this one is first row,
2nd column. This has to be 3. This is 2nd row, 1st column. The 2nd row, 1st
column is here so it will be 6. This is the 2nd row and 2nd column here is 7.
So this one here has to be 7. So it might seem to be funny, that hey, I’m
writing the same matrix but that’s what it is. The two matrices appear to be
the same if the order is the same and the elements are the same at the proper
I J location. First row and first column has to have the same as first row,
first column here. The first row, 2nd column has to be the same as first row,
2nd column here and so on so forth. It will make a lot more sense when we
talk about simultaneous equations- why we need to talk about two matrixes
being equal. And that’s the end of this segment. |