m by n matrix
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welcome to electron line in order to understand matrices better and to be able to work with them better we need to have the language damn so here we have a matrix in general format notice instead of having numbers in here we have simply the letter A representing of a number and the subscript here we have a sub 1 1 a sub 1 2 and so forth so what does that mean well remember again that the matrix has m rows and n columns so here there are 3 rows so in this case M is equal to 3 and theres three columns so therefore n is equal to 3
this is a 3 by 3 matrix also notice that the dimension of a matrix is term in term is mentioned in terms of M times n how many rows times how many columns in this case this would be a three by three matrix thats called the dimension of the matrix the numbers inside here are called elements matrix elements we also call them entries of the matrix a notice the subscripts tell you which element it is the first number in the subscript represents what row the element is in the second number represents what column it is in so in this case this is a row 2 column 1
so you go through a second row first column so this is a 2 1 heres a 2 3 that means the second row third column a 3 2 means the third row 2nd column a 1 3 means the first row and the third column so the first one always represents the row the second number represents the column and so thats how we term the matrices so we call the matrix elements or sometimes we call them matrix entries or entries of the matrix so we in general write a I J I the first number is the road that were in J the second number is the column that
in notice the numbers on the diagonal have the same row as they have the column number so this Row 1 column 1 Row 2 column 2 Row 3 column 3 and so thats what we call the diagonal line of the matrix so that helps you at least talk about the matrix when you read a book you can see when they talk about the elements are the entries talk about the dimension of the matrix they talk about the rows and the columns you now know what were talking about so lets stay to them and go look at the next video to get more explanations of what a matrix is
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