(1). We have, det(A) = 16 - 1 = 15 & trace(A) = 4+4 = 8
So, the characteristic equation of the matrix A is,
x² - x•trace(A) + det(A) = 0
So, x² - 8x + 15 = 0
So, (x - 3)(x - 5) = 0
So, x = 3, 5
So, the eigenvalues of A are 3 & 5
(2) det(A) = 4 - 9 = - 5 & trace(A) = 2 + 2 = 4
So, the characteristic equation of A is,
x² - x•trace(A) + det(A) = 0
So, x² - 4x - 5 = 0
So, (x - 5)(x + 1) = 0
So, x = - 1, 5
So, the eigenvalues of A are, - 1 & 5
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