By Géza Schay

ISBN-10: 0817683240

ISBN-13: 9780817683245

Building at the author's past version at the topic (*Introduction to**Linear Algebra*, Jones & Bartlett, 1996), this ebook bargains a refreshingly concise textual content appropriate for the standard direction in linear algebra, proposing a delicately chosen array of crucial issues that may be completely lined in one semester. even if the exposition normally falls in accordance with the fabric steered via the Linear Algebra Curriculum learn staff, it particularly deviates in offering an early emphasis at the geometric foundations of linear algebra. this offers scholars a extra intuitive figuring out of the topic and allows a neater seize of extra summary options lined later within the path.

The concentration all through is rooted within the mathematical basics, however the textual content additionally investigates a few fascinating functions, together with a piece on special effects, a bankruptcy on numerical equipment, and plenty of workouts and examples utilizing MATLAB. in the meantime, many visuals and difficulties (a entire recommendations handbook is offered to teachers) are integrated to augment and toughen knowing in the course of the e-book.

Brief but specified and rigorous, this paintings is a perfect selection for a one-semester direction in linear algebra detailed essentially at math or physics majors. it's a necessary software for any professor who teaches the subject.

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**Extra resources for A Concise Introduction to Linear Algebra**

**Example text**

We may take either one of the given points as P0 , and the vector AB as v. 60) or for the line L. 61) and eliminating t leads to the nonparametric equations x−2 y+3 z−5 = = . 62) 30 1. 63) or in scalar form x = 6 + 4t, y = 1 + 4t, z = −8 − 13t. 64) Hence the new nonparametric equations become y−1 z+8 x−6 = = . 65 look very diﬀerent, except for the denominators. We can check that they represent the same line by showing that the coordinates of A and B satisfy both. 66) 6−6 1−1 −8 + 8 = = = 0.

23. 32 1. Analytic Geometry of Euclidean Spaces P0 v u p0 tv S p - p0 P su p = p0 + su + tv O Fig. 23. 75) where s and t are appropriate real numbers. 75. So this is a parametric vector equation of S. 75, that is, S = {P : p = p0 + su + tv with t ∈ R} . 75 becomes the set of three scalar equations: x = x0 + su1 + tv1 , y = y0 + su2 + tv2 , z = z0 + su3 + tv3 . 5. (A Plane Through Two Lines). 3. 3. If we take P0 = (4, 3, 9), say, then S will be described by the equation p = (4, 3, 9) + s(2, −3, 7) + t(−1, 4, 2).

25. Of the line p = (3, 2, −4) + s(7, −5, 4) and the plane p = (0, −2, 1) + s(−3, 0, 3) + t(2, −3, 4). In the next six exercises ﬁnd the distances. 26. Between the point P0 (1, −2, 4) and the plane 3x + 2y − 2z = 3. 27. Between the point P0 (3, 4, 0) and the plane y − 2z = 5. 28. Between the lines p = (3, −2, 6) + s(−3, 5, 7) and p = (5, 1, 1) + t(−2, 1, 6). 29. Between the lines p = (2, 1, 5) + s(−4, 0, 3) and p = (0, −2, 3) + t(5, 0, −2). 30. Between the point P0 (3, 4, 0) and the line L : p = (3, −2, 6) + s(−3, 5, 7).

### A Concise Introduction to Linear Algebra by Géza Schay

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