tut7 - 2 Find an orthogonal matrix P and upper triangular...

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Math 235 Tutorial 8 Problems 1: For Q ( x,y,z ) = 5 x 2 - 4 xy - 8 xz + 8 y 2 - 4 yz + 5 z 2 , determine the corresponding symmetric matrix A . By diagonalizing A , express Q ( ~x ) in diagonal form and give an orthogonal matrix that diagonalizes A . Classify Q . 2: Classify the following symmetric matrices. a) ± - 1 2 2 - 5 ² b) 4 2 2 2 4 2 2 2 4 3: Let A = 1 0 0 0 0 - 1 0 1 -
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Unformatted text preview: 2 . Find an orthogonal matrix P and upper triangular matrix T such that P T AP = T . 4: Prove that if A is a positive definite symmetric matrix, then A is invertible. 5: Prove that if B is any invertible n × n matrix, then A = B T B is positive definite. 1...
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This note was uploaded on 01/27/2011 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

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