For example 1 2 3 4 9 e 0 0 0 5 from exercise 1 above

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Unformatted text preview: in a matrix are called its entries and are usually labeled with double subscripts: the first tells which row the element is in and the second tells which column it is in. The rows are numbered from top to bottom and the columns are numbered from left to right. Matrices themselves are usually denoted by uppercase letters (A, B , C , etc.) while their entries are usually denoted by the corresponding letter. So, for instance, if we have A= 3 0 −1 2 −5 10 then a11 = 3, a12 = 0, a13 = −1, a21 = 2, a22 = −5, and a23 = 10. We shall explore matrices as mathematical objects with their own algebra in Section 8.3 and introduce them here solely as a bookkeeping device. Consider the system of linear equations from number 2 in Example 8.1.2 (E 1) 2x + 3y − z = 1 (E 2) 10x − z = 2 (E 3) 4x − 9y + 2z = 5 We encode this system into a matrix by assigning each equation to a corresponding row. Within that row, each variable and the constant gets its own column, and to separate the variables on the left hand side of the equation fro...
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