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EGM 4350 FEM for MEs Spring 2019-Homework #01 Consider the following two three-dimensional vectors a and b 6 (a) Calculate the scalar product c-a b (b) Calculate the norm of vector a (c) Calculate the vector product of a and b A functionffxi,x2) of two variables x and x2 is given by ,22)2 2-12 (a) Multiply the matrices and express fas a polynomial in x and x2. (b) Determine the extreme (maximum or minimum) value of the function and corresponding x and x2 Consider the matrix equation [A]x)-Ib given by 一1 0111 0 -1 2 (a) Construct the quadratic form P(x)-x) r[A] { x-2 { x } r { b } . (b) Find (x)- (x \ by minimizing P(x) (c) Verify that the vector(x) satisfies [A] {x) = {b} . 4) Determine the eigen values and eigen vectors of the following matrice:s

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