Intermediate Mathematics for Economists (ECON2272) Tutorial 5. Quadratic Forms and Eigenvalues Solve all questions. A selection of questions will be marked. Question 1 Express the following quadratic forms as x'Ax where A is a symmetric matrix. (a) 5){:12 + 3x 4x32 (b) 2x} 9x; 3x +4x,x, 6x,x, +2x,X, (c) x;+2x3 5x.x, Question 2 Consider the matrix 2 =2 1 A= l 1 2 2 3 2 -2 Use the following two methods to show that A is an orthogonal matrix. a) Check that the columns of A form an orthonormal set of vectors. b) Check that A' =A