tut8 (1) - Math 235 Tutorial 8 Problems 1 Classify the...

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Unformatted text preview: Math 235 Tutorial 8 Problems 1: Classify the following: a) 1 −5 −5 1 b) Q(x) = 4x2 − 4x1 x2 + 5x2 1 2 2: For Q(x1 , x2 , x3 ) = 5x2 − 4x1 x2 − 8x1 x3 +8x2 − 4x2 x3 +5x2 , determine the corresponding 1 2 3 symmetric matrix A. By diagonalizing A, express Q(x) in diagonal form and give an orthogonal matrix that diagonalizes A. Classify Q. 3: Sketch the graph of 2x2 + 4x1 x2 − x2 = 4 showing both the original and new axes. 1 2 Find the equation of the asymptotes. 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 a positive definite symmetric matrix. 1 ...
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