symmetric matrix

Please do NOT send the answer back as an attachment. Thank you. What is the symmetic matrix of the quadratic form 2x^2 - 8xy + 4y^2?

vectors

Please do NOT send the answer back as an attachment. Thank you. The set of vectors {[ 1 -1] , [ 1 -1] , [ 2 -1] } [ 2 0 ] [ -1 0] [ -1 0] from M_2(R) is: A. linearly dependent B. linearly independent C. orthogonal D. a spanning set for M_2(R) E. a basis for M_2(R)

graph of quadratic equation

Please do NOT send the answer back as an attachment. Thank you. The graph of the quadratic equation x^T Ax = [0,0,1]x, where A = [ 1/(alpha^2) 0 0 ] [ 0 -1/(beta^2) 0 ] [ 0 0 0 ] is a(n): A. ellipse B. hyperbola C. elliptic paraboloid D. parabolic cone E. hyperbolic paraboloid

graph of a conic

Please do NOT send the answer back as an attachment. Please show work. Thank you. Identify and sketch the graph of the conic described by the quadratic equation x^2 + 4xy + y^2 - 12 = 0. Do this by writing this equation in matrix form; then change the equation to a sum of squares of the form x'^T Dx' where D is a diagonal matrix.

matrix

Please do NOT send the answer back as an attachment. Please show work. Thank you. For the problem, refer to the linear transformation T: R^3→R^3 given by T(x) = T(x, y, z) = (2x + 2z, x - y + z, 2x + 2z). Write the standard matrix representation , A = [T]_E, of T.