MATH221 December 2007
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Question 07 (b)
Consider the matrix . Find all eigenvalues of A.
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We already verified that 1 is an eigenvalue of A in part (a). To determine other possible eigenvalues, we solve for . We have
Let us make use of the fact that adding multiples of one row to another does not change the determinant to avoid lots of computation. Adding the second row of to the third, while subtracting times the second row from the first, yields the matrix
which has the same determinant has . By expanding down the first column, the determinant is
Therefore, the other eigenvalue of A is 2.
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