Download presentation
Presentation is loading. Please wait.
1
Lecture 11 Matrices and Linear Algebra with MATLAB
Dr .Qi Ying
2
Objectives Review Matrix Operations Review Linear Algebra
Linear systems of equations Matrix operations Solve linear systems of equations in MATLAB
3
Matrix Notation Principle diagonal
4
Matrix Notation Row vector and column vector
5
Matrix Terminology Diagonal matrix: square matrix where all elements off the main diagonal are zero Identity matrix: diagonal matrix where all elements on the main diagonal are equal to 1
6
Matrix Terminology Upper/lower triangular matrix
7
Matrix Terminology Banded matrix Tridiagonal matrix: Band width = 3
8
Matrix Operation Transpose: exchange rows for columns
9
Matrix Terminology Symmetric matrix: aij=aji or AT=A
10
Matrix Operation Addition/subtraction Must be of the same size
Perform operation element by element
11
Matrix Operation Multiplication with a scalar
The scalar is multiplied with each element to form a new matrix
12
Matrix Operation Multiplication with matrix
Number of columns in the first matrix must equal to the number of rows in the second matrix row1 Column 2
13
Matrix Operation In general, matrix multiplication is NOT commutative:
For square matrix:
14
Matrix Operation Matrix inversion: for square matrix
B is defined as the inverse of matrix A, or [B]=[A]-1
15
Matrix Operation Matrix inversion for 2x2 matrix
16
Linear systems of equations
17
Linear systems of equations
Solution of linear systems using MATLAB >> A=[5 3 2; 4 3 7; 7 5 1]; >> b=[7 9 5]'; >> x=inv(A)*b x = 3.1852 1.0370
18
Linear systems of equations
Check the results: >> x=A\b x = 3.1852 1.0370 >> A*x ans = 7.0000 9.0000 5.0000
19
Matrix Operation Matrix augmentation: adding one or more columns to the original matrix. Useful when we want to apply identical row operations on two matrices.
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.