e consider the problem -((1+x)))= 0 XE U(0) = 0, 'U(1)=\@Sind the analytical sol and he Find the Variational form and find Matrix A and b? consider the Variational form a (u,v)-(SV) where acu,v) = vdx prove that YVE H. (0,1),i=1, 2, \\-\ a(vi)=-v(x-1)+2V(xi)-(X;+1)] Where Vn is usual basis of hat functions. Consider the Problem Au=f and u= du=0 0 a with bilinear formalu,v) = SAU. AV r Prove that alu, v). V-ellPitic. and aluv) is continuous..

Find the component of the U along V U=(8,2), v=(3,-4)

Show that a counterclockwise rotation in R^2 through an angle α is described by the matrix Rα = (cos α − sin α)         (sin α cos α)

Let a = (-4, 3, 4) and b = (-5, 2, 3), then find the decomposition a = a +a of a with respect to b a = | help (vectors) aj =

Find all point of discontinuityz is a complex variable, z=x+iyf(z)=(1/z)-sec(z)

Let x(¹) (t) = -3t e 4e-3t, 0 x (²) (t) = [_5e-³]; x (³) (t) = -5e-3t, Are the vectors x(¹) (t), x(²) (t) and x(³) (t) linearly independent? choose ◆ If the vectors are independent, enter zero in every answer blank since those are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 0 -3t [8] = 0[*]+[-+* 0 [4e-3t -5e-3t -0[ + -5e-3t -35e-3t -5e-3t -35e-3t

z is a complex variable z=x+iyFind all points of discontinuityf(z)=(3z^2 +4)/(z^4 -16)

Find the coordinate vector of [*]B= = -(1-10--- 2 with respect to the basis B = for R³.

Vector u has POSITIVE x-component, POSITIVE y-component and ZERO z-component. Vector v has NEGATIVE x-component, POSITIVE y-component and POSITIVE z-component. What is true about u x v? There is not enough information to know anything. O It has NEGATIVE x-component, NEGATIVE y-component, NEGATIVE z-component O It has POSITIVE×-component, NEGATIVE y-component, NEGATIVE z-component It has POSITIVE x-component, NEGATIVE y-component, POSITIVE z-component

Which of the following sets of vectors in R' are linearly independent? (а) (-3,0,4), (5, -1,2), (1,1,3) (b) (-2,0,1), ((3, 2,5), (6, -1,1), (7,0, -2)