Question

(1) Matrices are entered row-wise. Row commas. Enter 1 2 3 (2) Element A, of matrix A is accesser (3) Correcting an entry is easy to (4) Any submatrix of Ais obtained by d row wise. Rows are separated by semicolons and columns are separated by spaces ner A l 23:45 6. B and hit the return/enter kry matrix A is accessed as A Enter and hit the returnerter key an entry is easy through indesine Enter 19 and hit the returnenter key, atrix of A is obtained by using rape secifiers for tow and column indices Enter B-A(2:3, 1:3) and hit the returnenter key. (5) The colon by its e colon by itself as a row or column index e s rows or columns of the matrix. Ent B-A(2:3, :) and hit the return/enter key. .2) and hit the Arow or a column of a matrix is deleted by settine it to a mul vector 1. Enter B return/enter key. (7) Matrices are transposed using the es are transposed using the single right quote character A. Enter A . Here is the transpose of the first row of -[1 2 3 4 5 6 7 the return/enter key. 91:and hit the return/enter key. Enter x A(1,:)'and hit (8) Matrix or vector products are well defined between compatible gairs. A row vector (x) times a column vector (x) of the same length gives the inner product, which is a scalar. But a column vector times a row vector of the same length gives the outer product, which is a matrix. Enter x' *x and hit the return/enter key (answer is a scalar). Now enter xx' and hit the return/enter key answer is a matrix). (9) It is very easy to multiply a vector with a matrix. Enter A*x and hit the return/enter key. (10)Also you can exponentiate a matrix if it is a square matrix. Enter A^2 and hit the return/enter key. (11)When a dot precedes the arithmetic operators and /. MATLAB performs array operation (element-by element operation). Enter A.^2 and hit the return/enter key. Note on Utility Matrices To aid matrix generation and manipulation, MATLAB provides many useful utility matrices (see the table given below). eye (m,n) Returns an m by n matrix with ones on the main diagonal zeros (m, n) Returns an m by n matrix of zeros ones (m,n) Returns an m by n matrix of ones rand (m, n) Returns an m by n matrix of random numbers randn (m, n) Returns an m by n matrix of normally distributed numbers diag (v) Generates a diagonal matrix with vector v on the diagonal diag (A) Extracts the diagonal of matrix A as a vector diag(A,1) Extracts the first upper off-diagonal vector of matrix A (12) eye (n) creates an nxn identity matrix. The commands zeros, ones, and rand work in a similar way. Now, to create a 3x3 identity matrix enter eye (3) and hit the return/enter key (13) You can create non-square matrices with ones on the main diagonal only. To create a 4x6 matrix with ones on the diagonal enter eye (4,6) and hit the return/enter key. (14)To create a 3x5 matrix of zeros, enter zeros (3,5) and hit the return/enter key. (15)Similarly to create a 5x8 matrix of ones, enter ones (5,8) and hit the return/enter key. (16)To create a 4x4 matrix of random numbers, enter rand (4,4) and hit the return/enter key.

on matlab

Answer 1

MATLAB:

1)

>> A=[1 2 3; 4 5 6; 7 8 9]
A =

1 2 3
4 5 6
7 8 9

2)

>> A(2,3)
ans = 6

3)
>> A(3,3)-9
ans = 0

4)
>> B=A(2:3,1:3)
B =

4 5 6
7 8 9

5)

>> B=A(2:3,:)
B =

4 5 6
7 8 9

6)

>> B(:,2)=[]
B =

4 6
7 9

7)

>> A=[1 2 3;4 5 6;7 8 9];

>> x=A(1,:)'
x =

1
2
3

8)

>> x*x'
ans =

1 2 3
2 4 6
3 6 9

>> x'*x
ans = 14

9)
>> A*x
ans =

14
32
50

10)

>> A^2
ans =

30 36 42
66 81 96
102 126 150

11)

>> A.^2
ans =

1 4 9
16 25 36
49 64 81

12)

>> eye(3)
ans =

Diagonal Matrix

1 0 0
0 1 0
0 0 1

13)

>> eye(4,6)
ans =

Diagonal Matrix

1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0

14)

>> zeros(3,5)
ans =

0 0 0 0 0
0 0 0 0 0
0 0 0 0 0

15)

>> ones(5,8)
ans =

1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1

16)

>> rand(4,4)
ans =

0.612710 0.872208 0.720667 0.570826
0.544332 0.556898 0.329526 0.529136
0.708312 0.665066 0.397935 0.717848
0.892258 0.995077 0.026875 0.834681

17)

>> K=[ones(3) zeros(3,2)]
K =

1 1 1 0 0
1 1 1 0 0
1 1 1 0 0

18)

>> K=[ones(3) zeros(3,2);zeros(2,3) 4*eye(2)]
K =

1 1 1 0 0
1 1 1 0 0
1 1 1 0 0
0 0 0 4 0
0 0 0 0 4

19)

>> diag(K)
ans =

1
1
1
4
4

20)

>> diag(K)'
ans =

1 1 1 4 4