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Unformatted text preview: the third row of X is [ − 2 0 1 ]A = [ − 2 1 5 ]. 10. (1). C is true since the eigenvalues are distinct. A is almost right: det A = ( − 1)3 × 1 ×
2 × 3 = − 6. B is true, the eigenvalues of an expression in A can be found from those of A
by substituting in the expression, so for example, the second eigenvalue of A2 + 6A− 1 is
22 + 6 × 2 − 1 = 7.
11. (4). A is false: it’s independent sets that are contained in bases, spanning sets contain a
basis. B is true since 5 > dim V . C is false: {X , 2X , 3X , 4X , 5X } surely doesn’t span.
12. (...
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This note was uploaded on 01/19/2010 for the course MAT MAT223 taught by Professor Uppal during the Spring '09 term at University of Toronto.
 Spring '09
 UPPAL
 Linear Algebra, Algebra, Vectors

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