The eigenvalues of a square matrix are defined by the condition that there be a nonzero solution to the homogeneous equation (A - XI)v=0. a. If there is a nonzero solution to the homogeneous equation (A - XI) v = 0, what can we conclude about the invertibility of the matrix A-XI? b. If there is a nonzero solution to the homogeneous equation (A - XI)v = 0, what can we conclude about the determinant det(A-XI)? c. Let's consider the matrix [1 [2 2] 1] from which we construct A- AI= [1 2 2 1] -A [1 0 0 1] = ['- .2 1 -A]. Find the determinant det(A-1). What kind of equation do you obtain when we set this determinant to zero to obtain det(A - XI) = 0?d. Use the determinant you found in the previous part to find the eigenvalues by solving det(A - XI) = 0. We considered this matrix in the previous section so we should find the same eigenvalues for A that we found by reasoning geometrically there. and find its eigenvalues by solving the e. Consider the matrix A = [2 0 1 2] and find its eigenvalues by solving the equation det(A - XI) = 0. f. Consider the matrix A = [0 1 01 0] and find its eigenvalues by solving the equation det(A - XI) = 0.