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Unformatted text preview: p ( x ) = det( xIA ) is a polynomial of degree n , say p ( x ) = ∑ n i =0 a i x i . Then p ( c ) = ∑ i a i c i . On the otherhand cIA ∈ M n ( F ) is a matrix with entries in F , and it is not obvious that the determinant of this matrix is ∑ i a i c i . 2. Problem 6 on page 101 of the text. 3. Problem 6 on page 107 of the text. The matrix A in the problem is to be viewed as the linear map T A : v 7→ Av on the space M 3 , 1 of column vectors. Also determine the eigenvalues and eigenspaces of T A . 4. Problem 4a on page 113. As in the third problem view the matrix A as the linear map T A when calculating eigenvectors. 1...
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This note was uploaded on 04/28/2010 for the course MATH 1B taught by Professor Aschbacher during the Winter '07 term at Caltech.
 Winter '07
 Aschbacher
 Linear Algebra, Algebra, Eigenvectors, Vectors

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