Compute the eigenvalues of matrix B, in terms of a, b and c, of the corresponding eigenvectors.

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Question 3

Consider the matrix

[-7 9 0

A-68 0

00 -1

(a)

Show, with working, that the eigenvalues of A are -1 and 2.

(6 marks)

(8 marks)

(b) Calculate the eigenvectors of the corresponding eigenvalues.

(c)

Suppose that a matrix B is diagonalizable and shares the same eigenvectors as matrix A. Given that

[-4a3 - 24c3 6a3 +24c3

0

0

-2

AB3 = -4a3-16c3 6a3 +16c3

0

0

Compute the eigenvalues of matrix B, in terms of a, b and c, of the corresponding eigenvectors.

(16 marks)

 

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