CHAPTER 01.10: INTRODUCTION: Equal Matrices

 

So letís 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 laymanís terms that means that, if the A matrix is M by N then B has to be M by N. They donít 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 letís look at an example. So somebody says ďHey, I got this A matrix here. 2, 3, 6, 7.Ē 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, Iím writing the same matrix but thatís 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 thatís the end of this segment.