Let A be the (2 x 2) matrix [(2k+1) (k-1)] A = (2k+2) (-k-2)]1 where kR...

 

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Let A be the (2 x 2) matrix [(2k+1) (k-1)] A = (2k+2) (-k-2)]1 where kR is a scalar. (a) Give the characteristic polynomial of A in terms of the scalar k. (b) Find a value for the scalar k = R so that A has an eigenvalue with algebraic multiplicity 2. [Hint: A degree 2 polynomial ax2 + bx + c has a double root if and only if the discriminant (b2-4ac) is zero.] Let A be the (2 x 2) matrix [(2k+1) (k-1)] A = (2k+2) (-k-2)]1 where kR is a scalar. (a) Give the characteristic polynomial of A in terms of the scalar k. (b) Find a value for the scalar k = R so that A has an eigenvalue with algebraic multiplicity 2. [Hint: A degree 2 polynomial ax2 + bx + c has a double root if and only if the discriminant (b2-4ac) is zero.]