ifiotdedepleamning di datsmachine vrartificialintelligencedx 1.2 Characteristic Equation [8pts] Consider the eigenvalue problem: Ax=x,x=0 where x is a non-zero eigenvector and is an eigenvalue of A. Prove the determinant AI=0. NOTE: There are many ways to solve this problem. You are allowed to use linear algebra propertie: as part of your solution. 1.3 Eigenvalues and Eigenvectors [5+10pts] 1.3.1 Eigenvalues [5pts] Given a matrix A : A=[abbc] (a) Find an expression for the eigenvalues of A in terms of a,b, and c. [4pts] (b) Find a simple expression for the eigenvalues if c=a. [1pt] 1.3.2 Eigenvectors [10pts] Given a matrix A : A=[x312x] (a) Calculate the eigenvalues of A as a function of x (calculation process required). [3pts] (b) Find the normalized eigenvectors of matrix A (calculation process required). [7pts]