Matlab (Linear algebra)

function plot2d(X) % plot2d Two dimensional plot. % X is a matrix with 2 rows and any number of columns. % plot2d(X) plots these columns as points in the plane % and connects them, in order, with lines. % The scale is set to [-10, 10] in both directions. % % For example, the statement X=house creates % a sample matrix X representing common figures. % Then, for various 2 by 2 matrices A, % plot2d(A*X) % demonstrates the effect of multiplication by A. x = X(1,:)'; y = X(2,:)'; plot(x, y, 'ro', x, y, 'g-'); axis([-10 10 -10 10]) axis('square') 

function X = house % X = house stores the "house" data set in X. % % The "house" data set is for use with plot2d. % Try plot2d(A*X) for various 2 by 2 matrices A. % % See also hand. X = [ -6 -6 -7 0 7 6 6 -3 -3 0 0 -6 -7 2 1 8 1 2 -7 -7 -2 -2 -7 -7 ]; 

LAB 3: LU Decomposition and Determinants In this lab you wil use MATLAB to study the following topics: The LU decomposition of an invertible square matrix A. . How to use the LU decomposition to solve the system of linear equations Ax b. Comparison of the computation time to solve Ax - b by Gaussian elimination vs. solution by LU decomposition of A. . The determinant of a square matrix, how it changes under row operations and matrix multiplication, and how it can be calculated efficiently by the LU decomposition . The geometric properties of special types of matrices (rotations, dilations, shears). LAB 3: LU Decomposition and Determinants In this lab you wil use MATLAB to study the following topics: The LU decomposition of an invertible square matrix A. . How to use the LU decomposition to solve the system of linear equations Ax b. Comparison of the computation time to solve Ax - b by Gaussian elimination vs. solution by LU decomposition of A. . The determinant of a square matrix, how it changes under row operations and matrix multiplication, and how it can be calculated efficiently by the LU decomposition . The geometric properties of special types of matrices (rotations, dilations, shears)