C nulla r6 and cola r4 d nulla r4 and cola r6

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Unformatted text preview: : Quiz 1a -- Solutions Page 3 Linear Mathematics 1 0 Quiz 1a -- Solutions 0 1 Page 4 1 0 , 2 , 0 , . Which one of the following statements is 13. Consider the set U = 0 3 0 0 correct? a) U is a basis of R3 . b) U is linearly independent but does not span R3 . c) U spans R3 but is not linearly independent. d) U does not span R3 and U is not linearly independent. Solution c) 14. The eigenvalues of the matrix M = 1 8 are -1 and 5. 1 3 Find a matrix which diagonalises M. a) -4 2 1 1 1 1 -4 2 4 2 1 1 1 1 4 -2 b) c) d) Solution a) 15. Let A be an n n diagonalisable matrix. Which one of the following is true? a) The columns of A are linearly independent. b) A has no repeated eigenvalues. c) All the entries in A that are not on the main diagonal are zero. d) There exists a basis for Rn consisting of eigenvectors of A. Solution d) Math 2061: Quiz 1a -- Solutions Page 4...
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This note was uploaded on 02/06/2012 for the course MATH 2061 taught by Professor Notsure during the Three '09 term at University of Sydney.

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