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Matrix in Matlab

Creating Matrix (or two dimensional array) of different sizes in Matlab. How to show a particular entry of a matrix. Transpose, size and inverse of a matrix.


Q 1. Create the following one row matrix


>> A = [3 4 8] (press Enter)
ans =
     3  4  8


Q 2. Create the following two row matrix


>> A = [1 2 3; 4 5 6] (press Enter)
ans =
     1  2  3
     4  5  6


Q 3. Create the following three row matrix


>> A = [1 2 3; 4 5 6; 7 8 9] (press Enter)
ans =
     1  2  3
     4  5  6
     7  8  9


The general form of a 3x3 matrix (matrix with 3 rows and 3 columns) is

a11 means element at row-1 and column-1
a12 means element at row-1 and column-2
a32 means element at row-3 and column-2
and son on...

Now, consider the above 3x3 matrix


>> A (1,1) (press Enter)
ans =
     1

It shows the element in the row-1 and column-1




>> A (2,3) (press Enter)
ans =
     6

It shows the element in the row-2 and column-3




>> A (3,2) (press Enter)
ans =
     8

It shows the element in the row-3 and column-2




>> A (1,:) (press Enter)
ans =
     1  2  3

It shows the elements in the row-1




>> A (3,:) (press Enter)
ans =
     7  8  9

It shows the elements in the row-3




>> A (:,2) (press Enter)
ans =
     2
     5
     8

It shows the elements in the column-2




>> A (:,3) (press Enter)
ans =
     3
     6
     9

It shows the elements in the column-3




>> A (2,1:2) (press Enter)
ans =
     4 5

It shows the elements in the row-2 from 1 to 2




>> A (3,2:3) (press Enter)
ans =
     8  9

It shows the elements in the row-3 from 2 to 3




>> A (1:2,2) (press Enter)
ans =
     2  5

It shows the elements in the column-2 from 1 to 2




>> A (2:3,1) (press Enter)
ans =
     4  7

It shows the elements in the column-1 from 2 to 3



Size of a Matrix


>> size (A) (press Enter)
ans =
     3  3

It shows size of the matrix A which is 3 3 (3 rows and 3 columns)



Diagonal of a Matrix


>> diag (A) (press Enter)
ans =
     1
     5
     9

It shows elements in the diagonal of matrix A.



Transpose of a Matrix


>> A' (press Enter)
ans =
     1  4  7
     2  5  8
     3  6  9

It converts row-1 into column-1, row-2 into column-2 and so on..



Inverse of a Matrix

Using Matlab find inverse fo the matrix.


>> A = [1 2 9; 0 3 6; 2 5 1];
>> B = inv (A) (press Enter)
B =
     0.4737    -0.7544    0.2632
     -0.2105    0.2982    0.1053
     0.1053    0.0175    -0.0526

It shows inverse of the matrix A.



Now show that A*B = I (Where I is identity matrix).


>> A*B (press Enter)
ans =
     1    0    0
     0    1    0
     0    0    1

It shows that (matrix)*(inverse of matrix) = Identity matrix.

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