Unformatted text preview: MEC702 Wk 8 Tutorial Matrices
1. Find a.) A + B , b.) A − B , c.) 2A, d.) 2A − B and e.) B + 21 A.
−1
2 −1
,B=
;
−1
−1 8 1
4
6 −1
4 , B = −1 5 ;
(b) A = 2
−3 5
1 10 (a) A =
1
2 2. Find a.) AB and b.) BA (if they are dened).
1 2
2 −1
,B=
;
2 4
−1 8 1 1 2
1 −1 7
A = 2 −1 8 , B = 2 1 1;
1 −3 2
3 1 −1
−1 3
1 2
A = 4 −5, B =
;
0 7
0
2 0 −1 0
2
A = 4 0 2, B = −3.
8 −1 7
1
1 0 3 −2 4
1 6
A=
,B=
.
6 13 8 −17 20
4 2 (a) A =
(b)
(c)
(d)
(e) 3. Find the inverse of the matrix (if it exists).
1
(a)
3
1
(b)
2 1
(c) 3
3
2
;
7
−2
;
−3
1
5
6 1
4;
5 1 4. Find (a) the characteristic equation, (b) the eigenvalues, and (c) the corresponding eigenvalues of the matrices below.
a.)
4
2
2
c.)
3
−5
−3 b.)
2
2
2
2
1
0
2
d.)
4
5
3 Coversion to Systems
Find the general solution to the given ODE by rst converting it into a system.
1. y 00 + 3y 0 + 2y = 0.
2. y 000 + 2y 00 − y 0 − 2y = 0. Review on Higher Order Linear ODE
Solve the given ODE. Show the details of your work.
1. y iv − 3y 00 − 4y = 0.
2. y 000 + 4y 00 + 13y 0 = 0.
3. y 000 − 4y 00 − y 0 + 4y = 30e2x .
4. (D4 − 16I)y = −15 cosh x.
5. x2 y 000 + 3xy 00 − 2y 0 = 0. 2 ...
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 Winter '16
 Alveen Chand
 Linear Algebra, Matrices, Characteristic polynomial, Complex number, Order Linear ODE

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