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# lecture_2 - MA 35100 LECTURE NOTES WEDNESDAY JANUARY 13...

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MA 35100 LECTURE NOTES: WEDNESDAY, JANUARY 13 Matrices Let’s say that we have the following collection of equations: 3 x + 21 y - 3 z = 0 - 6 x - 2 y - z = 62 2 x - 3 y + 8 z = 32 The Chinese created shorthand notation for such a system of equations. They placed them in a rectangular array, called Fang Cheng , as follows: 3 21 - 3 0 - 6 - 2 - 1 62 2 - 3 8 32 Nowadays we place the numbers in an array called a matrix : 3 21 - 3 0 - 6 - 2 - 1 62 2 - 3 8 32 | {z } four columns three rows This particular matrix has three rows and four columns, so it is called a 3 × 4 matrix (read “three by four matrix.”) In general, say that we have a collection of equations: a 11 x + a 12 y + a 13 z = a 14 a 21 x + a 22 y + a 23 z = a 24 a 31 x + a 32 y + a 33 z = a 34 The numbers a 11 , a 12 , . . . are called the coefficients , and we may place them in a 3 × 4 matrix as follows: A = a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 . The entries of the matrix are denoted by a ij , where the first subscript i denotes the row and the second subscript j denotes the column. The entry a ij is located in the i th row and the j th column.

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