# PS3 - the eigenvalues of A 2 3 For each A specify for what...

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MATH 580: Problem Set 3 due Thursday, September 30, 2004 1. Are the following matrices invertible? If so, calculate the inverse. B = ± i 1 - 1 i ² ; P = ± 3 a 1 4 ² (for P , specify for which values of a the inverse P - 1 exists). 2. Consider the matrix A = ± 4 8 1 2 ² (a) ﬁnd the eigenvalues of A , and the transformation matrix T which diagonalizes A ; (b) ﬁnd the eigenvalues of the matrix B = AA A 2 ; (c) in general, if A is a n × n matrix with eigenvalues { λ i } , what are
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Unformatted text preview: the eigenvalues of A 2 ? 3. For each A , specify for what b the equation Ax = b has a solution: A = ± 2 3 14 21 ² ; C = ± 1 13-8 ² ; D = ε ε ε ε ε ε 2 ε , where ε ∈ R (as usual, use the Euclidean inner product). 4. Keener 1.2.3 (p.51) 5. Keener 1.2.6 - b,c (p.51) 6. Find the Moore-Penrose pseudoinverse of A = ± 1 8 ² ....
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