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UCF EGN 3420 - EGN 3420 Final

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EGN 3420 Final Dr. Fernando Gonzalez Fall 2005 NAME 1. Given the following matrices compute the following: =4355A −=7421B =6231C a. The product AB =AB b. The inverse1−A 1−A=c. The characteristic equation of A )(λ∆= d. The eigenvalues of A 21,λλ=e. The eigenvectors of A 21, XX = f. The scalar λ and the vector X that satisfies XAXλ=. X,λ= g. Show that 1−C does not exist. h. Show that the 2 vectors in C linearly dependent.2. Use the Gaussian Elimination algorithm to solve the following system of linear equations. 5013345624843232131−=−=+−=++xxxxxxx3. Find the line that best fits the data below. x F(x) 1 2 2 3 3 5 4 6 5 124. Find the curve, )(2xP , that passes through all points. Then compute )5.2(2P x F(x) 1 2 2 3 3 55. Find the integral ∫=91)( dxxfI using Simpson’s 1/3 and 3/8 rules and the following set of points. x )(xf 1 1 2 2 3 3 4 2 5 1 6 2 7 3 8 5 9 46. Find dxxdf )(at 3=xusing the following set of points. Use the centered finite divided difference equation using an increment of 1 and 2 then use Richardson’s Extrapolations to compute the answer with an error proportional to )(4hO x )(xf 1 1 2 2 3 4 4 7 5


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UCF EGN 3420 - EGN 3420 Final

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