QUESTION 1 (15 pts). Consider the matrix 10 -4 0 A = -4 26 -8 8 10 (i) Show that A is positive definite using the Gershgorin Circle Theorem and properties of the matrix A (without computing eigenvalues). (ii) Factorize the matrix A as QAQ, where Q is orthogonal and A diagonal, using the Spectral Theorem. Show your work. (iii) Draw on the same graph the Gershgorin disks Di, i = 1, 2,3, and the eigenvalues M, i = 1,2,3, computed in (ii), and verify that A1, 12, As ( Up_Di. (iv) Calculate the norms || All1, ||All2, ||All- (v) Calculate Al/2