By Constance Reid

ISBN-10: 0486436136

ISBN-13: 9780486436135

This energetic consultant by means of a widespread historian specializes in the function of Euclid's *Elements* in mathematical advancements of the final 2,000 years. No mathematical heritage past easy algebra and aircraft geometry is important to understand the clear and straightforward causes, that are augmented via greater than eighty drawings. 1963 variation.

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B = n • p, and expanding Equation (3). The alternative point-normal fOrm is "J. (x 1 p 1) + ~(x2 Pz) + ·· · + a,(x,. - p,) 0. r This is a generalization of the equation a; + bx;, - c (which describes a line in R2) and a; + b~ + ~ - d (which describes a plane in R3). ) Note that a linear equation contains no products of variables (such as xf or x1x:z) or functions of variables (such as sin Xp e>'2, ,'%4) other than multiplication by a constant scalar. For example, 3x1 Sx 1x2 I 2x2 = 1 and 3x y2 = 7 are not linear equations.

Step 3{a). Obtain a leading 1 in the second row, third column. There is one there already. Step 3(11). Obtain zeros in the: other positions in the third column by adding appropriate multiples of the second row to the other rows. Replace: the first row with the sum of itself and 1 times the second row. Then replace: the third row with the sum of itsdf and - 1 times the second row: 1 2 0 2 5] [ 0 0 1 2 3 0 0 0 0 0 Step 3{c). Place: any newly created zero rows at the bottom of the matrix. It is already there.

Ii. 2 are, respectivdy, l: 0 0 1 0 0 1 -~] [" 0 0 and 3 1 2 0 0 1 1 0 Each is in row-reduced echdon form. EXAMPLE 6 n The matrix 1 2 0 0 0 -1 1 2 0 0 0 0 0 0 0 0 ~] 00 is in row-reduced echdon form. EXAMPLE 7 00 The matrices l: n n 1 0 1 0 0 [: [~ ~l and [~ 0 0 ~J are not in row-reduced echelon form. ) 00 As we have said, the basic goal of the matrix dimination procedure is to transform, by means of a systematic sequence of dementary row operations, the original augmented matrix into one that is in row-reduced echelon form.

### A Long Way from Euclid by Constance Reid

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