Matrices are simply tables of numbers, but the rise of modern computing has made them increasingly important in science, economics, computer science, and mathematics. Matrices have their own notation and form, and their own unique arithmetic which you’ll need to become familiar with before proceeding further. Once you understand the mechanics, the computations are straightforward, and your calculator can even do them for you! Matrices have many applications, and we’ll see how they tie together with systems of equations later in this unit.
A MATRIX is a rectangular array of numbers or algebraic expressions enclosed in square brackets. (Some math texts use parentheses instead.) Usually, a matrix is denoted by a capital letter. The plural of matrix is matrices. Each matrix has ROWS and COLUMNS. In mathematics we are very precise: rows are horizontal, and columns are vertical. If matrix M has 2 rows and 3 columns, we say the dimensions of M are 2 3, or M is a 2 by 3 matrix. m2,1 is the ENTRY in the second row and first column of matrix M; in general, mr, c is the entry in the rth row and cth column.
Two matrices can be added only if they have the same dimensions.
We can multiply matrices of any size as long as they "fit " right. You get the entries of the product matrix by finding "sums of products " of rows of the first matrix with columns of the second. Here is a more formal description:
To get the r,c entry of the product matrix, multiply the corresponding entries in the rth row of the first matrix and the cth column of the second matrix and add the products.
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