Exercise: Let A = [[1, 2, 0], [0, 2, 0], [-1, 0, 0]] Verify that the characteristic polynomial of A is C_A(位) = -位(位 - 1)(位 - 2) Thus, the eigenvalues of A are 位 = 0, 位 = 1, and 位 = 2. Find bases for the three eigenspaces E_0, E_1, and E_2 and state the algebraic multiplicity and geometric multiplicity of each eigenvalue of A. For 位 = 0, we have A - 位I = A and so E_0 = Null(A). A basis for the eigenspace E_0 is B_(E_0) = {[[0], [鈼籡]}.