Suppose that A is a 5x5 matrix and cA(lambda)=(lambda-1)(lamda^2-lamda-6)(lambda^2+1) Answer the three questions: 1) The

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Suppose that A is a 5x5 matrix and
cA(lambda)=(lambda-1)(lamda^2-lamda-6)(lambda^2+1)
Answer the three questions:
1) The rank of 2I -A is?
2)Let W denote the solution set to the system A(x1 x2 x3 x4
x5)=5(x1 x2 x3 x4 x5). Which of the following must be always
true?
a)W contains exactly only one vector
b)W has infinitely many vectors
c)W has more than one, but only finitely many vectors
d)W contains exactly one nonzero vector
e)None
3)If the rank of I-A is at most 2, then
a) The rows of 3I-A are linearly independent
b) I-A can be transformed by EROs to I
c)A is not invertible
d)A is diagonalizable
e)None