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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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