Слайд 2
LECTURE 9
MATRIX ALGEBRA AND SIMULTANEOUS LINEAR EQUATIONS
Temur Makhkamov
Indira Khadjieva
QM Module Leader
Слайд 3Lecture outline
The meaning and properties of matrices;
The arithmetic operations on matrices;
The applications
of matrices to reality
Слайд 4Matrix
A Matrix is simply a rectangular array of numbers arranged in rows
and columns.
The size of a matrix is indicated by the number of its rows and the number of its columns
The whole matrix is labeled by a capital letter
The individual numbers (elements) contained in the matrix are labeled by lower case letters with a suffix to identify their locations within the matrix.
Слайд 5Examples of matrices
Examples:
1) – 2x2 matrix
2) – 2x3 matrix
3) – ?
Слайд 6Addition (and Subtraction) of matrices
You can add (subtract) two matrices of
the same size (equal number of rows and columns).
The sum (difference) of two equal-sized matrices results in the new matrix of the same size as the two matrices being added.
Example:
Слайд 7Exercise: Addition and Subtraction
Слайд 8Scalar multiplication
Multiply each element of the matrix by the number.
Example:
Слайд 9Exercise: Scalar multiplication
Слайд 10Matrix multiplication
Two matrices can be multiplied only if the number of columns
of the 1st matrix equals to the number of the rows of the 2nd matrix.
Multiply rows of the 1st matrix by columns of the 2nd matrix
Example:
Слайд 11Matrix Transpose
The transpose of matrix can be obtained by interchanging the rows
and columns
The first row of the matrix A is the first column of matrix A transposed
Слайд 12Zero & Identity matrix
Zero matrix is a matrix with all elements 0.
Identity
matrix is a square matrix with elements of 1s on the main diagonal from top left to bottom right and 0s on other positions
Слайд 13Determinant of a matrix
A numerical value of matrix
Can be a negative number
Exists
for a square matrix only
Determinant for 2x2 matrix is calculated as follows:
Слайд 14Inverse of a (2x2) matrix (1)
If then
Слайд 15Inverse of a (2x2) matrix (2)
Example: , then
Calculate:
Check: