Download PDF by Stewart Venit, Wayne Bishop, Jason Brown: Elementary Linear Algebra, First Canadian Edition

By Stewart Venit, Wayne Bishop, Jason Brown

ISBN-10: 0176440763

ISBN-13: 9780176440763

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Additional resources for Elementary Linear Algebra, First Canadian Edition

Example text

Through P(2, -1) with normal n = (0, 2) 30 CHAPTER 1 r;e,_try ofJl2 ""J Jl3 11. Through P(- 2, 5) and perpendicular to the line x + 2y = 5 12. Through P(1, - 3) and perpendicular to the line 3x - 4y 1 In Exercises 13-21 give a point-parallel or two-point form, and para11etric equations for t~e 1 2 or 1 3 line described. 13. Through P(2, 1, - 3) and parallel to v 14. Through P(3, 1) and parallel to v (1, 2, 2) = (2, 3) 15. Through P(2, -3, 1) and parallel to the x>-axis 16. Through P(1, 2, -1) and Q(2, -1, 3) 17.

D+ kb, (4) which says that (sl' ~· ... ) satisfies Equation (3). Now assume that (sl' -'2• ... , s11) satisfies the ttansformed system. This implies that Equation (4) holds. We also know that Equation (1) is satisfied, so that ~s1 + ~-7. + · · · + a,s,. = b. s,) = kb. s,. d, 00 as desired. 2 Exercises In Exercises 1-6 determine isl1ear. J, 3-X:z - "3 - 4 x1 - x4 = 1- ~ x 1 I x4 I x 3 2 - 1 x+2xy-y-o - sin-X;z = x1 I - ~ I X:z - or not the ginn system of equations 2. 2x - \ly + X+ 2y- =0 3. 3x- xy 5.

If we start with three noncoplanar vectors u, v, and w, we have an analogous situation. The set of all linear combinations x = x(r, s, t) of u, v, and w given by x = ra I sv I tw is the 3-space determined by a, v, and w. Even if planes or 3-spaces do not contain the origin, a similar procedure can be used to obtain their equations: We first "translate" one of the points to the origin, cre-ating vectors with the same magnitude and direction as the directed line segments beginning at this point (Figure 4).

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Elementary Linear Algebra, First Canadian Edition by Stewart Venit, Wayne Bishop, Jason Brown

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