Math54samplemidterm2 - SAMPLE MIDTERM II MATH 54 SEC.1,...

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SAMPLE MIDTERM II MATH 54 SEC.1, FALL 2009 80 POINTS, 80 MINUTES Question 1, 18 pts True or false? No justiFcation necessary. Correct answers carry 1 . 5 points, incorrect answers carry 1 . 5 points penalty. However, you will not receive a negative total score on any group of 6 questions. T ± If A is diagonalizable, then so is A 2 . T ± The columns of a diagonalizable matrix are linearly independent. T ± If A is an n × n diagonalizable matrix, then each vector in R n can be written as a linear combination of eigenvectors of A . T ± If the square matrix A is singular, then 0 must be an eigenvalue of A . T ± The eigenvalues of an upper triangular matrix are exactly the diagonal entries. T ± Each eigenvector of an invertible matrix A is also an eigenvector of A - 1 . T ± A vector v and its negative - v have equal lengths. T ± If u and v are orthogonal, then || u + v || 2 = || u || 2 + || v || 2 . T ± If λ is a real eigenvalue of the orthogonal matrix A , then λ = ± 1.
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This note was uploaded on 02/10/2010 for the course MATH 54 taught by Professor Chorin during the Fall '08 term at University of California, Berkeley.

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