By Ron Larson, David C. Falvo
The cornerstone of undemanding Linear Algebra is the authors' transparent, cautious, and concise presentation of material--written in order that scholars can absolutely know how arithmetic works. This application balances concept with examples, purposes, and geometric instinct for an entire, step by step studying system.The 6th version comprises up to date insurance of laptop Algebra platforms (Maple/MATLAB/Mathematica); extra help is equipped in a corresponding expertise advisor. information and functions additionally mirror present statistics and examples to interact scholars and exhibit the hyperlink among idea and perform.
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Additional info for Elementary Linear Algebra (incl. Online chapters)
If you are using a graphing utility, your screens for Example 2(c) may look like those shown below. com/pic/larsonELA6e. 1, you used Gaussian elimination with back-substitution to solve a system of linear equations. You will now learn the matrix version of Gaussian elimination. The two methods used in the next example are essentially the same. The basic difference is that with the matrix method there is no need to rewrite the variables over and over again. EXAMPLE 3 Using Elementary Row Operations to Solve a System Linear System x Ϫ 2y ϩ 3z ϭ 9 Ϫx ϩ 3y ϭ Ϫ4 2x Ϫ 5y ϩ 5z ϭ 17 Add the first equation to the second equation.
3x Ϫ y ϭ 3 6x ϩ 2y ϭ 1 32. 33. 2x Ϫ 8y ϭ 3 34. 9x Ϫ 4y ϭ 5 1 2x 35. 8 The symbol indicates an exercise in which you are instructed to use a graphing utility or a symbolic computer software program. 4x Ϫ 5y ϭ 3 Ϫ8x ϩ 10y ϭ 14 1 2x ϩ 13 y ϭ 0 36. 75 12 Chapter 1 Sy stems of Linear Equations 58. 75w ϭ In Exercises 37–56, solve the system of linear equations. 37. x1 Ϫ x 2 ϭ 0 3x1 Ϫ 2x2 ϭ Ϫ1 38. 3x ϩ 2y ϭ 2 6x ϩ 4y ϭ 14 39. 2u ϩ v ϭ 120 u ϩ 2v ϭ 120 40. x1 Ϫ 2x2 ϭ 0 6x1 ϩ 2x2 ϭ 0 41. 9x Ϫ 3y ϭ Ϫ1 1 42.
Find a polynomial function p of degree 2 or less that passes through the points ͑0, 1͒, ͑2, 3͒, and ͑4, 5͒. Then sketch the graph of y ϭ 1͞p͑x͒ and compare this graph with the graph of the polynomial function found in Exercise 8. 10. Calculus The graph of a parabola passes through the points ͑0, 1͒ and ͑12, 12 ͒ and has a horizontal tangent at ͑12, 12 ͒. Find an equation for the parabola and sketch its graph. 11. Calculus The graph of a cubic polynomial function has horizontal tangents at ͑1, Ϫ2͒ and ͑Ϫ1, 2͒.
Elementary Linear Algebra (incl. Online chapters) by Ron Larson, David C. Falvo