001 Introduction (153.33 MB)
001 Coordinate systems and coordinates in the plane and in the 3-space (122.57 MB)
002 Slope-intercept equations of straight lines in the plane (70.38 MB)
003 Normal equations of planes in the 3-space (63.91 MB)
004 Vectors (56.19 MB)
005 Scalars (48.22 MB)
006 Vector addition and vector scaling (105.48 MB)
007 Linear combinations (165.54 MB)
008 Matrices (41.67 MB)
009 Linear transformations (398.02 MB)
010 Matrix—vector multiplication (60.13 MB)
011 Rules for computations with real numbers (59.47 MB)
012 Pythagorean Theorem and distance between points (66.55 MB)
013 Sine, cosine, and pythagorean identity (31.79 MB)
014 Cosine Rule (55.02 MB)
001 Different ways of looking at equations (33.63 MB)
002 Solution set (58.54 MB)
003 Linear and non-linear equations (63.27 MB)
004 Systems of linear equations (26.96 MB)
005 Solution sets of systems of linear equations (54.77 MB)
006 An example of a 2 x 2 system of linear equations, a graphical solution (31.21 MB)
007 Possible solution sets of 2 x 2 systems of linear equations (42.65 MB)
008 Possible solution sets of 3 x 2 systems of linear equations (38.26 MB)
009 Possible solution sets of 3 x 3 systems of linear equations (52.6 MB)
010 Possible solution sets of 2 x 3 systems of linear equations (24.82 MB)
011 Possible solution sets of m x n systems of linear equations (40.92 MB)
001 Our earlier problem revisited an algebraical solution (182.33 MB)
002 Three elementary operations (70.77 MB)
003 What is Gauss—Jordan elimination and Gaussian elimination (47.87 MB)
004 Gauss—Jordan elimination, a 2-by-2 system with unique solution (38.68 MB)
005 The same example solved with Gaussian elimination and back-substitution (30.12 MB)
006 The same example solved with matrix operations coefficient matrix and augmented (66.82 MB)
007 How to write the augmented matrix for a given system of equations, Problem 1 (258.05 MB)
008 How to write system of equations to a given augmented matrix, Problem 2 (148.11 MB)
009 Gaussian elimination, Problem 3 (558.28 MB)
010 Gaussian elimination, Problem 4 (376.41 MB)
011 Gaussian elimination, Problem 5 (312.42 MB)
012 Gaussian elimination, Problem 6 (315.33 MB)
013 What happens if the system is inconsistent (36.28 MB)
014 Gaussian elimination, Problem 7 (122.99 MB)
015 Preparation to the general formulation of the algorithm REF and RREF matrices (285.04 MB)
016 How to read solutions from REF and RREF matrices (419.2 MB)
017 General formulation of the algorithm in Gauss–Jordan elimination (473.32 MB)
018 Gauss–Jordan elimination, Problem 8 (312.68 MB)
019 Gauss–Jordan elimination, Problem 9 (191.99 MB)
020 Gaussian elimination, Problem 10 (112.24 MB)
021 Gauss–Jordan elimination, Problem 11 (406.45 MB)
022 Gauss–Jordan elimination, Problem 12 (520.49 MB)
023 Gauss–Jordan elimination, Problem 13 (566.79 MB)
001 Solving systems of linear equations in Linear Algebra and Geometry (94.07 MB)
002 Solving systems of linear equations (Calculus) Problem 1 (143.97 MB)
003 Solving systems of linear equations (Calculus) Problem 2 (206.19 MB)
004 (Optional from 2230) Solving systems of linear equations (Calculus) Problem 3 (513.72 MB)
005 Solving systems of linear equations (Calculus) Problem 4 (572.23 MB)
006 Problem 5 (Chemistry) (277.27 MB)
007 Problem 6 (Electrical circuits) (270.56 MB)
001 Introduction to matrices (55.11 MB)
002 Different types of matrices (51.47 MB)
003 Matrix addition and subtraction, Problem 1 (27.23 MB)
004 Matrix scaling, with geometrical interpretation (33 MB)
005 Matrix scaling, Problem 2 (57.25 MB)
006 Matrix multiplication, with geometrical interpretation (110.63 MB)
007 Matrix multiplication, how to do (41.55 MB)
008 Matrix multiplication, Problem 3 (35.28 MB)
009 Matrix multiplication and systems of equations, Problem 4 (49.96 MB)
010 Transposed matrix, definition and some examples (75.79 MB)
011 Trace of a matrix, definition and an example (20.22 MB)
012 Various matrix operations, Problem 7 (238.82 MB)
013 Various matrix operations, Problem 8 (287.18 MB)
001 Properties of matrix operations, an introduction (41.73 MB)
002 Matrix addition has all the good properties (32.07 MB)
003 Matrix multiplication has a neutral element for square matrices (119.76 MB)
004 Matrix multiplication is associative (282.36 MB)
005 Matrix multiplication is not commutative (43.95 MB)
006 Sometimes commutativity happens, Problem 1 (309.55 MB)
007 Two distributive laws (163.69 MB)
008 Matrix multiplication does not have the zero-product property (17.53 MB)
009 There is no cancellation law for matrix multiplication (26.92 MB)
010 Inverse matrices not all non-zero square matrices have an inverse (68.61 MB)
011 Inverse matrix for 2-by-2 matrices non-zero determinant (129.29 MB)
012 Solving matrix equations, Problem 2 (343.3 MB)
013 Powers of matrices powers of diagonal matrices (19.24 MB)
014 Computation rules for transposed matrices (139.38 MB)
015 Supplement to Video 83 Inverse of a product (118.61 MB)
016 Inverse of a transposed matrix (26.83 MB)
017 Various rules, Problem 3 (223.39 MB)
001 Inverse matrices, introduction to the algorithm (406.27 MB)
002 Algorithm for inverse matrices, an example (57.55 MB)
003 Matrix inverse, Problem 1 (289.45 MB)
004 Matrix inverse, Problem 2 (204.71 MB)
005 Matrix equations, Problem 3 (250.36 MB)
006 Matrix equations, Problem 4 (155.95 MB)
007 Matrix equations, Problem 5 (341.83 MB)
008 Matrix equations, Problem 6 (437.57 MB)
009 Matrix inverse, Problem 7 (387.07 MB)
010 Elementary operations and elementary matrices (71.57 MB)
011 Inverse elementary operations and their matrices (35.05 MB)
012 A really important theorem (67.09 MB)
013 Four equivalent statements (148.25 MB)
001 Formally about the number of solutions to systems of linear equations (348.6 MB)
002 Two more statements in our important theorem (136.69 MB)
003 Solution of a linear system using A inverse, Problem 1 (334.86 MB)
004 Determining consistency by elimination, Problem 2 (465.18 MB)
005 Matrix equations, Problem 3 (278.16 MB)
001 Why the determinants are important (68.48 MB)
002 2-by-2 determinants notation for n-by-n determinants (47.88 MB)
003 Geometrical interpretations of determinants (104.8 MB)
004 Geometrically about the determinant of a product (68.66 MB)
005 Definition of determinants (101.96 MB)
006 Conclusion 1 Determinant of matrices with interchanged columns (54.05 MB)
007 Conclusion 2 What happens when one column is a linear combination of others (248.51 MB)
008 Conclusion 3 About adding a multiple of a column to another column (72.17 MB)
009 Conclusion 4 Determinant of kA for any k ∈ R (43.03 MB)
010 Elementary column operations (208.11 MB)
011 How to compute 2-by-2 determinants from the definition (56.53 MB)
012 How to compute 3-by-3 determinants from the definition (82.36 MB)
013 Sarrus' rule for 3-by-3 determinants (444.26 MB)
014 Determinant of transposed matrix row operations (76.32 MB)
015 Evaluating determinants by cofactor expansion along rows or columns (621.39 MB)
016 Evaluating determinants by row or column reduction (156.51 MB)
017 Determinant of inverse (31.7 MB)
018 Properties of determinants, Problem 1 (100.97 MB)
019 Properties of determinants, Problem 2 (124.14 MB)
020 Properties of determinants, Problem 3 (190.43 MB)
021 Determinant equations, Problem 4 (175.6 MB)
022 Determinant equations, Problem 5 (301.98 MB)
023 Determinant equations, Problem 6 (36.97 MB)
024 Determinant equations, Problem 7 (29.85 MB)
025 Invertible matrices, determinant test with a proof, Problem 8 (331.85 MB)
026 Cramer's rule, a proof, an example, and a geometrical interpretation (206.73 MB)
027 Cramer's rule, Problem 9 (231.82 MB)
028 Inverse matrix, an explicit formula (199.93 MB)
029 Invertible matrices, Problem 10 (180.07 MB)
030 Problem 11, a large determinant (43.08 MB)
031 Problem 12, another large determinant (537.57 MB)
032 Problem 13 a trigonometric determinant (203.05 MB)
033 Problem 14 Vandermonde determinant (456.43 MB)
001 Vectors, a repetition (55.29 MB)
002 Computation rules for vector addition and scaling (108.46 MB)
003 Computations with vectors, Problem 1 (172.33 MB)
004 Computations with vectors, Problem 2 (131.76 MB)
005 Computations with vectors, Problem 3 (105.22 MB)
006 Parallel vectors, Problem 4 (143.21 MB)
007 Parallel vectors, Problem 5 (158.18 MB)
008 Linear combinations, Problem 6 (52.62 MB)
009 Linear combinations, Problem 7 (69.45 MB)
010 Linear combinations, linear independence, Problem 8 (311.63 MB)
011 Linear combinations, linear dependence, Problem 9 (327.52 MB)
012 Area, Problem 10 (104.58 MB)
013 Midpoint of a line segment, Problem 11 (178.33 MB)
001 Norm of a vector, Problem 1 (197.63 MB)
002 Properties of the norm (112.82 MB)
003 Distance between points, Problem 2 (178.17 MB)
004 Unit vectors, how to normalize a vector (50.02 MB)
005 Unit vectors in given direction, Problem 3 (104.93 MB)
001 Different products for vectors (42.02 MB)
002 Perpendicular straight lines and orthogonal vectors (52.18 MB)
003 Orthogonal projections (36.53 MB)
004 Definition of dot product for geometrical vectors (58.11 MB)
005 How to compute dot product, an example (257.46 MB)
006 Dot product for vectors in R^n orthogonality and angles (48.61 MB)
007 Properties of dot product (165.23 MB)
008 Angles between vectors, Problem 1 (147.37 MB)
009 Angles between vectors, Problem 2 (297.99 MB)
010 How to find vector orthogonal to a given vector in the plane or in the 3-space (24.53 MB)
011 Orthogonal projections and decompositions (33.49 MB)
012 Orthogonal projections and decompositions, Problem 3 (118.48 MB)
013 Orthogonal projections and decompositions, Problem 4 (121.05 MB)
014 Orthogonal sets, Problem 5 (213.1 MB)
015 Orthogonal projections and decompositions, Problem 6 (85.36 MB)
001 Cross product, an introduction (24.87 MB)
002 Cross product, how it is defined (170.59 MB)
003 Three properties of cross product (315.27 MB)
004 The length of the cross product of two vectors (132.05 MB)
005 More properties of cross product (170.28 MB)
006 Cross product Problem 1 (138.57 MB)
007 Cross product in the plane (31.5 MB)
008 Scalar triple product and volume (42.05 MB)
009 Scalar triple product, Problem 2 (91.5 MB)
010 Collinearity in the plane and coplanarity in the 3-space (64.57 MB)
011 Determinant test for vectors, Problem 3 (149.85 MB)
001 Lines in the plane, an introduction (52.49 MB)
002 Slope-intercept and intercept form (182.24 MB)
003 Normal equation (222.31 MB)
004 Parametric equations (291.78 MB)
005 Determinant equation (136.06 MB)
006 Lines in the plane, Problem 5 (278.17 MB)
001 Planes in the 3-space, an introduction (20.49 MB)
002 Normal and intercept equation (179.21 MB)
003 Parametric equations (322.05 MB)
004 Parametric to normal (283.56 MB)
005 Normal to parametric find a point and two parallel vectors for a given plane (252.29 MB)
006 Determinant equation (188.25 MB)
007 Planes Problem 6 (171.16 MB)
001 Lines in the 3 space, an introduction (41.5 MB)
002 Lines in the 3 space, Problem 1 (132.26 MB)
003 Lines in the 3 space, Problem 2 (153.13 MB)
004 Lines in the 3 space, Problem 3 (102.75 MB)
001 Incidence 1 points and planes (52.58 MB)
002 Incidence 2 planes and lines (157.57 MB)
003 Incidence 3 points and lines (243.72 MB)
004 Parallel and orthogonal objects (47.38 MB)
005 Parallel planes, Problem 4 (126.89 MB)
006 Parallel planes Problem 5 (76.06 MB)
007 Orthogonal planes Problem 6 (186.97 MB)
008 Planes and lines, Problem 7 (165.29 MB)
009 Planes and lines, Problem 8 (194.46 MB)
010 Planes, Problem 9 (191.93 MB)
011 Planes, lines, and systems of equations, Problem 10 (276.67 MB)
001 Distances between sets, generally (63.75 MB)
002 Distance between points and planes (37.39 MB)
003 Distance between points and planes, Problem 1 (163.41 MB)
004 Distance between points and planes, Problem 2 (254.24 MB)
005 Distance between points and lines (25.42 MB)
006 Distance between points and lines, Problem 3 (222.41 MB)
007 Distance between points and lines, Problem 4 (212.56 MB)
008 Distance between (skew) lines (57.75 MB)
009 Distance between (skew) lines, Problem 5 (524.52 MB)
010 Distance between (skew) lines, Problem 6 (303.66 MB)
001 Linear Algebra and Geometry 1, Wrap-up (34.96 MB)
002 Linear Algebra and Geometry 2, some words about it (37.46 MB)
003 Final words (11.36 MB)
001 Bonus Lecture (39.42 MB)