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Welcome to the world of Matrices Sections 4-1 and 4-2 How do we define a matrix? • A matrix is a rectangular array of numbers written within a bracket. • A matrix is represented by a capital letter. • A matrix is classified first by the number of rows and then by the number of columns in the matrix. Let’s look at a few examples This matrix has 2 rows and 1 column so its dimension is a 2x1 This matrix has 1 row and 3 columns so its dimension is a 1x3 This matrix has 3 rows and 3 columns so its dimension is a 3x3 Each number in a matrix is a matrix element You can identify a matrix element by its position in the matrix Use a lower case letter with a subscript to represent the matrix element’s row number and column number The lower case letter corresponds to the name of the matrix and the subscript represent the row and column in which the number appears. Let’s look at some examples A= the first element is a11 = 2 the second element is a21 = 1 B= b11 = 7, b12 = 4, b13 = 2 c11 = c23 = c13 = c3 2= c21 = c1 2= C= We can only add or subtract matrices that have the same dimensions + We can add these matrices because they have the exact same dimensions All we do is add corresponding elements and put the answers into a new matrix with the same dimensions. 4+2 =6 17 +1 = 18 The new matrix is Now for the fun stuff…doing the actual addition and subtraction Another example…