MEC702_Wk_8_Tutorial

# MEC702_Wk_8_Tutorial - MEC702 Wk 8 Tutorial Matrices 1 Find...

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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 dened).     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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