Please do part b), c) and d). Do not answer part a). -1 4 -2Consider the matrix A =-3 4-3 1323 are eigenvectors of A. Find the corresponding eigenvalues.(a) The vectors i = |1 and j:%3D(b) A = 3 is an eigenvalue of A. Find an eigenvector of A with this eigenvalue.(c) The matrix A is diagonalizable. Using your answers to parts (a) and (b) above, write down an invertiblematrix P and a diagonal matrix D such that A = PDP-1.(d) Circle whichever of the following are equal to A100 (no justification necessary; this question may havemultiple correct answers):[(-1)100 4100(-3)100 4100(-3)100 1100(-2)100701003100PD100 p-1;p100 D100 (p-1)100,(PDP-1)100 keyAndwerFor part (a), the eigenvalue for is d = 1 (since A = #) and the eigenvalue for j is A = 2 (sinceAj25). For part (b), the eigenvectors of A with eigenvalue A = 3 (found by solving the equation(A – 31) = 0) are all the nonzero multiples of 3/[1/4]so any one of these is a correct answer. For part(c), one possible diagonalization of A is A = PDP-1 where[1 2 1]P = 1 31 3 4[1 0 0]D = 0 2 00 0 3[1/4]other correct answers are possible (here I scaled the 3-eigenvector 3/4 to clear fractions). Finally, for1part (d), only the second and fourth options (PD100 p-1 and (PDP¯1)100) are equal to A100.1

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(b) A = 3 is an eigenvalue of A. Find an eigenvector of A with this eigenvalue. (c) The matrix A is diagonalizable. Using your answers to parts (a) and (b) above, write down an invertible matrix P and a diagonal matrix D such that A = PDP-1. (d) Circle whichever of the following are equal to A100 (no justification necessary; this question may have multiple correct answers): (-1)100 4100 (-2)1007 |(-3)100 4100 |(-3)100 0100 3100 PD100 p-1; p100 p100 (P-1)100, (PDP-1)!00. 100