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## civil sem4 m iv assignments .pdf

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Applied Mathematics (AM-IV)
Assignments
 Assignment No. 1
1. Find the Eigen values and Eigen vectors of the matrix.
matrix
8 −8 −2
A= 4 −3 −2
3 −4 1
2 2 1
2. If A= 1 3 1 find
find the characteristics roots &amp; characteristics vector &amp; A3+I.
1 2 2
−1
3. If A= 0
0

2 3
3
3 5 find the Eigen values &amp; A +5A+8I.
0 −2

Update:

Nilesh Deokar
9821540802

Bhushan Borole
9892703175

8097260574

 Assignment No. 2
1. Verify Cayley-Hamilton
amilton theorem for the matrix A And hence find A-3 &amp; A4 where
1
2 −2
A = −1 3
0
0 −2 1
2. Apply Cayley-Hamilton
amilton theorem to A =
And deduce that A8 = 625I.

1 2
2 −1

1 0 0
3. If A = 1 0 1 show that for every integer n ≥3
0 1 0
An = An-2+A2-II hence find A50.
1
4. Verify the matrix A = 2
0
A-2.

2
0
−1 0 satisfy the characteristics equation .Hence find
0 −1

Update:

Nilesh Deokar
9821540802

Bhushan Borole
9892703175

8097260574

 Assignment No. 3
8 −8 −2
1. Show that the matrix A = 4 −3 −2 is diagonalizable. Find the Transforming
3 −4 1
matrix &amp; the diagonal matrix.
−9 4 4
2. Show that the matrix A = −8 3 4 is diagonalizable. Find the diagonal form D
−16 8 7
&amp; the diagonalising M.
−2
3. Reduce the following matrix to diagonal form A = 2
−1
diagonalising matrix.

2 −3
1 −6 &amp; the
−2 0

1 0 0
4. If A = 1 0 1 find A50.
0 1 0

Update:

Nilesh Deokar
9821540802

Bhushan Borole
9892703175

8097260574

 Assignment No. 4
7
4
1. A = 4
7
−4 −4

−1
−1 show that it is derogatory.
4

1
2. Show that A = 1
1

0 0
−1
1 0 derogatory and polynomials.
0 1

2
3. Show that the matrix A = 1
1
polynomial.

−2 3
derogatory. Also find its minimal
1
1 is non-derogatory.
3 −1

4. Define the followings:
I. Derogatory &amp; non-derogatory
non
matrix.
II.
State Cayley-H
Hamilton theorem.
III.
Minimal polynomial.
IV.
Monic polynomial.

Update:

Nilesh Deokar
9821540802

Bhushan Borole
9892703175

8097260574

 Assignment No. 5
1. Type of co-relation?
2. Define different method for ungrouped data to find co-efficient
fficient of co-relation?
co
3. Solve this by Actual mean method?
X:
2
3
4
7
6
Y:
10
7
3
1
2
4. Solve the previous one by using Step-deviation
S
method?
X:
1
2
3
4
5
Y:
30
40
50
60
70
5. Find the co-efficient
efficient of co-relation
relation for the price By Assumed Mean method?
X:
100 98
85
92
90
84
88
90
93
95
Y:
500 610 700
630
670
800
800
750
700 690

Update:

Nilesh Deokar
9821540802

Bhushan Borole
9892703175