The basic point of this part is to formulate systems of linear equations in
terms of matrices. We can then view them as analogous to an equation like \(7x =
5\).
In order to use them in systems of equations we will need to learn the algebra
of matrices; in particular, how to multiply them and how to find their inverses.
Geometrically, a linear equation in \(x\), \(y\) and \(z\) is the equation of a plane.
Solving a system of linear equations is equivalent to finding the intersection
of the corresponding planes.
Last Modification: 2020-09-17 Thu 11:47
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- Part B: Matrices and Systems of Equations | 1. Vectors and Matrices | Multivariable Calculus | Mathematics | MIT OpenCourseWare
Captured On [2020-02-05 Wed 21:18] Source Session 10: Meaning of Matrix Multiplication | Part B: Matrices and Systems of Equations | 1. Vectors and Matrices | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: What represent matrix multiplication
Figure 2: Matrix identity and plane rotation by matrix multiplication
Figure 3: Continuous apply of rotation by matrix multiplication
2 Can we use the distributive law with matrix multiplication?...
Captured On [2020-02-05 Wed 21:19] Source Session 11: Matrix Inverses | Part B: Matrices and Systems of Equations | 1. Vectors and Matrices | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: Inverse Matrix
Figure 2: Inverse Matrix formula
Figure 3: Inverse Matrix Formula: Minors and cofactors
Figure 4: Inverse Matrix Formula: Transpose and Divide by \(\det(A)\)
2 How can we solve a small squared linear system?...
Captured On [2020-02-05 Wed 21:20] Source Session 12: Equations of Planes II | Part B: Matrices and Systems of Equations | 1. Vectors and Matrices | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: Equations of Planes
Figure 2: Point in the plane
Figure 3: Normal vector and vectors on the plane
Figure 4: Extract normal vector from plane equation
Figure 5: Check vector parallel or perpendicular to a plane...
Captured On [2020-02-05 Wed 21:21] Source Session 13: Linear Systems and Planes | Part B: Matrices and Systems of Equations | 1. Vectors and Matrices | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: 3x3 Linear System
Figure 2: Possible solutions to linear systems (2)
2 How many solutions we can get from a linear system? 2.1 Front How many solutions we can get from a linear system?...
Captured On [2020-02-05 Wed 21:22] Source Session 14: Solutions to Square Systems | Part B: Matrices and Systems of Equations | 1. Vectors and Matrices | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: Trivial solution and inverse of a matrix
Figure 2: Solutions of homogeneous linear system
Figure 3: Coplanar normal vectors
Figure 4: General case of solutions
2 When can we say that a linear system has an unique solution?...
Captured On [2020-02-05 Wed 21:13] Source .Session 9: Matrix Multiplication | Part B: Matrices and Systems of Equations | 1. Vectors and Matrices | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: What is a matrix?
Figure 2: Change coordinate systems
Figure 3: Entries in matrix multiplication
Figure 4: Nmemotecnic rule for matrix multiplication
2 How we can set up 2 matrix for its multiplication? 2.1 Front How we can set up 2 matrix for its multiplication?...