Algebra by Cohn P. M.

By Cohn P. M.

Studies very important history in algebra and introduces extra complex themes, emphasizing linear algebra and the homes of teams and jewelry. contains extra labored difficulties and an entire set of solutions to the routines. additionally good points extended proofs and extra in-depth remedies of affine areas, linear programming, duality, Jordan general shape and team concept.

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Example text

Give the coordinates of T. 1 . P ( 1, - 2 ) 4. P(-2, -2) 2. P(-2,2) 5 . P ( - 1, - 3 ) 3. P(2,2) 5 . P ( 0 ,- 3 ) In Exercises7 through2S, draw a sketch of the graph of the equation. 4 f * 9 Y 2 : 3 6 22. Y' : 41cs 25. xz*y',:O 2 8 . y':x-3 'I.. y : l r l - 5 2 0 . 4 x 2- 9 Y ' : 3 6 L4. x: 23. ( 2 x + V - l ) ( 4 V + r 2 ) : 0 Y: \81 y:5 y:lx-51 y--lxl+z A:4x3 3x2- L3xy- L0y2: g xa- 5x2yI 4y2: g +):O 29. Draw a sketch of the graph of each of the following equations: (a) V: lzx (b\ v : -{2x (c) y' :2x 30.

If ll is not parallel to L and iJ & is any constant,the equation A'x 'l Bry I C' * k(A"x * Bry * C") :0 represents an unlimited number of lines. Prove that eadr of these lines contains the point of intersection df lr and t. 29. Given an equation ot It is 2x 'f 3y - 5: 0 and an equation of l, is 3x + 5y - 8 : 0, by using Exercise 28 and without finding the coordinates of the point of intersection of ,r and lr, find an equation of the line through this point of intersection and (a) passing through the point (1, 3); (b) parallel to the r axis; (c) parallel to the y axis; (d) having slope-2; (e) perpendicular to the line having the eqtatio\ 2x + y :7; (f) forming an isoscelestriangle with the coordinate axes.

The Point P is on the line segmentbetween points Pl(1 ,3) and Pr(6,2) and is three times as far from Pr as it is frcmpr. 21. The Point P i8 on the line through P' and P, and is three times as far ftom Pr(6, 2) as it is from P, (1,3) but is not between Pr and Pr. 22. The Point P is on the Une though P, and P, and is three times as far from P1(1, 3) as it is ftom Pr(6,2) but is not between P1and P2. 23. The point P is on the line through Pr(-3,5) and Pr(-L,2) so that ppr : + . ,pr. 24. Find an equation whose graph is the circle that is the set of all points that are at a distance of 4 units from the point (1, 3).

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