Q1. If you are given that 0 is an eigenvector of A = (a) [5 marks]...

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Q1. If you are given that 0 is an eigenvector of A = (a) [5 marks] find the constants a and b in A; (b) [10 marks] construct a matrix P such that A 4 -1 2 - 2 a 4 a do co PDP-¹ with diagonal matrix D; (c) [5 marks] determine A is positive or negative definite or semidefinite, or indefinite, and explain. (d) [5 marks] deduce the eigenvalues and eigenvectors of C = A² – 2A + I, where I is the identity matrix. [Note: Do not attempt to compute the matrix C]. Q1. If you are given that 0 is an eigenvector of A = (a) [5 marks] find the constants a and b in A; (b) [10 marks] construct a matrix P such that A 4 -1 2 - 2 a 4 a do co PDP-¹ with diagonal matrix D; (c) [5 marks] determine A is positive or negative definite or semidefinite, or indefinite, and explain. (d) [5 marks] deduce the eigenvalues and eigenvectors of C = A² – 2A + I, where I is the identity matrix. [Note: Do not attempt to compute the matrix C].

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