HW01_Solution

# HW01_Solution - EML 4507 Finite Element Analysis Design...

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EML 4507 Finite Element Analysis & Design Fall 2010 HW01 Solution 3. Consider the following two three–dimensional vectors a and b : {1, 4, 6} and {4, 7, 2} TT ab (a) Calculate the scalar product c = a b . (b) Calculate the norm of vector a . (c) Calculate the vector product of a and b Solution: (a) 1 4 4 7 6 2 44 c ; (b) 2 2 2 1 4 6 53 a (c) 1 4 6 (8 42) (2 24) (7 16) 34 22 9 4 7 2 i j k a b i j k i j k 7. Calculate the inverse of the matrix [ A ] in Problem 6. Solution: 1 1 71 4 2 7 2 7 2 11 22 11 3 7 3 4 3 4 3 2 4 7 2 3 22 22 11 A 8. Matrices [ A ] and [ B ] are defined below. If B = A −1 , determine the values of p, q, r and s . 2 4 3 1 2 [ ] 1 2 3 , [ ] 3 3 1 5 6 1 p q r s AB . Solution: If 1 BA , then I . 11 2 ( 3) 4 3 ( 1) 1 p 5 p 31 ( 3) 5 3 6 0 q 3 q

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22 1 1 2 ( 3) 3 1 r AB 2 r 23 1 2 2 ( 1) 3 0 s 0 s 9. Solve the following simultaneous system of equations using the matrix method: 12 4 3 3 33 xx Solution: The given system can be represented by matrix form as follows, 1 2 4 3 3 1 3 3 x x 1 1 2 4 3 3 3 3 3 0 1 1 3 3 1 4 3 1 4 3 3 1 x x 11. Find the eigen values and eigen vectors of the following matrices: (a)
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HW01_Solution - EML 4507 Finite Element Analysis Design...

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