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Class Notes for Mathematics at University of Toronto Scarborough (UTSC)

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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 2: Linear Combination, Psa Tu Engine, Unit Vector

OC5374889 Page
27 Jan 2016
89
Mata23 - lecture 2 - vectors in euclidian spaces continued. Geometric interpretation in r2: see diagram 1. (cid:126)v rn, (cid:126)v rn such that (cid:
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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 1: Asteroid Family, Scalar Multiplication, Vector Algebra

OC5374883 Page
27 Jan 2016
105
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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 12: Row And Column Spaces, Gaussian Elimination, A127 Road

OC5374888 Page
12 Feb 2016
89
Mata23 - lecture 12 - bases, dimensions, spaces, and nullity. Is a basis of w1 by theorem. |ri r, i = 1, 2, 3. Is linearly independent (not a basis for
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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 11: Linear Independence, Solution Set, Scalar Multiplication

OC5374884 Page
11 Feb 2016
90
Mata23 - lecture 11 - homogeneousness, linear dependance, and bases. Linear dependence: let s = {(cid:126)v1, (cid:126)v2, . , (cid:126)vk} be a set of
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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 8: Elementary Matrix, Augmented Matrix, European Route E40

OC5374886 Page
29 Jan 2016
58
Mata23 - lecture 8 - consistency, inverses, and elementary row matrices. Consistency: a linear system having no solutions is inconsistent. If it has on
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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 5: Scalar Multiplication, Main Diagonal, The Young Turks

OC5374883 Page
27 Jan 2016
71
Mata23 - lecture 5 - properties of matrix operations. Matrix symmetry continued: example 5: let matrix a = [aij] mn,n(r). Show that a + at is symmetric
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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 6: Linear System, Row Echelon Form, Coefficient Matrix

OC5374886 Page
27 Jan 2016
68
A11 b2 bm: remark: the linear system #1 is equivalent to a(cid:126)x = (cid:126)b with #2, a is called the coef cient matrix of system #2, and. [a|(cid
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UTSCMATA37H3Smith( G)Spring

MATA37H3 Lecture Notes - Lecture 4: In C, Antiderivative

OC5374882 Page
27 Jan 2016
201
Mata37 - lecture 4 - integrability reformulation and inde nite integrals. Want to show  > 0, p of [a, b] s. t. U (f, p ) l(f, p ) <  is false, or  >
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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 3: Triangle Inequality

OC5374884 Page
27 Jan 2016
67
Mata23 - lecture 3 - cosine law and inequalities. Cosine law: the angle between two nonzero vectors (cid:126)u and (cid:126)v in rn is arccos( (cid:126
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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 7: Augmented Matrix, Free Variables And Bound Variables, Row Echelon Form

OC5374883 Page
27 Jan 2016
78
Mata23 - lecture 7 - back substitution and the gauss-jordan method. Gauss method with back substitution: example 6: using gauss method with back substi
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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 4: Diagonal Matrix, Triangular Matrix, Coefficient Matrix

OC5374885 Page
27 Jan 2016
70
Mata23 - lecture 4 - inequalities, matrices, and linear systems. Inequalities: example 12 (continued): show that in r2 the nonzero vector (cid:126)n =
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UTSCMATA23H3Chrysostomou( G)Spring

MATA23H3 Lecture Notes - Lecture 10: Solution Set, Elementary Matrix, Selenium

OC5374886 Page
5 Feb 2016
70
Mata23 - lecture 10 - invertiblity, homogeneousness, and subspaces. Invertible matrices continued: example 6: assume that matrices a, b and a + b are i
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