Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

LEARNING LINEAR ALGEBRA USING
MATLAB 

1


Advice 
• Nobody
 could
 or
 would
 want
 to
 know

everything
about
MATLAB
...


• Use
the
Help
files
...


• Be
 prepared
 for
 frustraEon,
 but  if  you  need 
MATLAB it is worth the frustra?on
...
  Prac?ce 
more
...
A vector will have only one row or one column
...
A row vector is entered row-wise with
consecutive elements of a row separated by a
space or a comma
...

a=[1,2,3,4,6,4,3,4,5] or
a=[1 2 3 4 6 4 3 4 5]
Answer is:
a=
1

2

3

4

6

4

3



4

5
4


Column Vector 
Elements in a column vector are separated
by a semicolons
...

Example:
v=[1;3;5;6]
Answer:
v=
1
3
5
6



5


• Now let us add 2 to each element of ‘a’ vector 
and store the result in a new vector ‘b’
...


The
enEre
matrix
must
be
enclosed
within
square

brackets
...
0000
0
...
0000i 5
...
0000i



8


Con?nua?on 
• If
it
is
not
possible
to
type
the
enEre
input
on
the

same
 line,
 then
 use
 three  consecu?ve  periods 
(…)
to
signal
conEnuaEon
and
conEnue
the
input

on
 the
 next
 line
...


MATLAB Command

Answer

A=
1
5

A=[1 3 4;5 10
...
 
• For  a  complex  matrix  C,  Ct=C’  produces  the 
conjugate transpose 
Find the transpose of the following matrices
using MATLAB




11


MATLAB Command:
A=[1 2 3;7 8 9;10 11 12];
B=A'
Answer
B=
1 7
2 8
3 9

10
11
12

MATLAB Command
C=[12 3 4-8*i;5*i 10 15];
Ct=C'

Answer
Ct =
12
...
0000i
3
...
0000
4
...
0000i 15
...
* operator
...
*B
2/11/10


ANSWER
C=
1 4 0
4 25 -10
0 -10 1

Soori
Prashant
Kumar


14


Inverse of a Matrix 

MATLAB Command
A=[5 -1;10 -1];
B=inv(A)
Output
B=
-0
...
0000

0
...
0000



15


To prove that Inverse of a matrix ‘A’ multiplied
by ‘A’ matrix gives Identity Matrix
MATLAB Command
A=[5 -1;10 -1];
B=inv(A);
I=inv(A)*A
Output
I=
1 0
0 1



16


Exponen?a?on 

MATLAB Command:
A=[1 0 2;2 4 5;1 2 2];
B=A^3

Output:
B=
17 28 38
101 172 228
47 80 106




17


More
operaEons

• diag(v)
 Generates
 diagonal
 matrix
 with
 vector

‘v’
on
the
diagonal
...


• diag(A,1)
 extracts
 the
 first
 upper
 off‐diagonal

vector
of
matrix
A







18


MATLAB Command
B=[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]
diag(B)‘
Output
B=
1 1
1 1
1 1
0 0
0 0
ans =
1 1

1
1
1
0
0

0
0
0
4
0

0
0
0
0
4

1

4

4



19


MATLAB Command
B=[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]
diag(B,1)‘
B=
1
1
1
0
0
ans =
1

1
1
1
0
0

1
1
1
0
0

0
0
0
4
0

1

0

0

0
0
0
0
4




20


Watch and understand 
MATLAB Command:
d=[1 5 7 9];
d1=[2 2 2];
d2=[-1 -1];
D=diag(d)+diag(d1,1)+diag(d2,-2)
D=
1
0
-1
0

2
5
0
-1

0
2
7
0

0
0
2
9



21


To find the determinant 
Find the determinant of A
MATLAB Command
A=[1 0 1;0 2 4;3 3 0];
det(A)
ans =
-18



22


To find the eigenvalue  
Find the eigenvalue of A
MATLAB Command
A=[2 -2;-2 5];
eig(A)
ans =
1
6




23


To find the coefficients of the characteris?c polynomial 

• The
 “poly”
 funcEon
 generates
 a
 vector
 containing
 the

coefficients
of
the
characterisEc
polynomial
...

These
are
actually
the
eigenvalues
of
the

given
matrix
...
8944 -0
...
4472 0
...
7417




26


More Stuff 
– help
svd

– help
QR

– help
LU

– help
rref

– help
rcond

– help
cond





27




---