EGN 3420 Final Dr Fernando Gonzalez NAME 1 Given the following matrices compute the following 5 5 1 2 1 3 A B C 3 4 4 7 2 6 a The product AB b The inverse A 1 AB A 1 Fall 2005 c The characteristic equation of A d The eigenvalues of A 1 2 e The eigenvectors of A X1 X 2 f The scalar and the vector X that satisfies AX X X 1 g Show that 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 4 x1 8 x3 4 2 x1 6 x 2 x3 45 3x 2 13x3 50 3 Find the line that best fits the data below x 1 2 3 4 5 F x 2 3 5 6 12 4 Find the curve P2 x that passes through all points Then compute P2 2 5 x 1 2 3 F x 2 3 5 9 5 Find the integral I f x dx using Simpson s 1 3 and 3 8 rules and the 1 following set of points x 1 2 3 4 5 6 7 8 9 f x 1 2 3 2 1 2 3 5 4 df x at x 3 using the following set of points Use the centered finite dx divided difference equation using an increment of 1 and 2 then use Richardson s Extrapolations to compute the answer with an error proportional to O h 4 6 Find x 1 2 3 4 5 f x 1 2 4 7 12
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