Course Overview

Course Outline Solving Systems of Linear Equations Identify linear equations, solve systems of linear equations, and explore cases with no solution or infinite solutions.   Eignenvalue Decomposition Graphically explore eigenvectors
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Review – Eigenvalue Decomposition

Visualizing Eigenvectors When you multiply a matrix and its eigenvector, the eigenvector is simply scaled, and the scaling factor is the eigenvalue.     The eig Function     For
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Eigenvalues and Eigenvectors of a Matrix

What are Eigenvalues and Eigenvectors?  A matrix can be represented by its eigenvalues and eigenvectors. This representation is called the eigenvalue decomposition. Eigenvalues and eigenvectors come in sets. The key
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Limitations

Special Cases All the systems of equations shown so far have had the same number of equations as unknowns. This means the coefficient matrix A is square. Also, solving them
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The Backslash Operator

Plot and Solve a System of Linear Equations Task 1  In this activity, you will find the point in intersection between two lines: y=6−x y=2+3x Use the linspace function to
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Preparing Systems

Review: Matrix-Vector Multiplication Matrix Dimensions Two matrices being multiplied must have compatible dimensions. The inner dimensions of the matrices being multiplied must agree. The result has size equal to the
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Linear Equations and Systems

What Makes an Equation Linear?  All equations can be classified as either linear or nonlinear.   Linear Equations A linear equation has only two types of terms: constants, and variables
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Review – Interpolation

Summary: Interpolating Data   Interpolation Methods for interp1 method Interpolation method used 'linear' [Default] Linear interpolation. 'spline' Cubic spline interpolation. 'pchip' Cubic polynomial interpolation preserving increasing/decreasing property of data. 'next'
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