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ptest2 - P 1 = 1 2 P 2 = 2 1 P 3 =-1-1(b P 1 = 1 P 2 = 2 1...

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Practice Test 2 for 1502KB 1. Find the inverse, if it exists, of the following matrices ( a ) 1 2 2 2 1 2 2 2 1 ( b ) 1 - 1 0 2 0 - 1 1 1 2 ( c ) 1 1 0 0 1 1 1 0 1 ( d ) 0 1 0 1 2 0 2 0 1 1 1 0 0 2 2 2 2. Find the eigenvalues and the associated eigenvectors of the following matrices ( a ) 1 2 2 1 ( b ) 1 - 1 1 1 ( c ) 0 1 2 - 1 ( d ) 1 1 0 0 1 1 1 0 1 3. Let u = 1 3 . Find v if v is generated by rotating u (a) counterclockwise by angle π 4 . (b) clockwise by angle π 6 . (c) counterclockwise by angle π 2 and then clockwise by angle π 3 . 4. Let v = 3 1 , Find vector u R 2 such that v is generated by rotating u (a) counterclockwise by angle π 4 . (b) clockwise by angle π 6 . (c) counterclockwise by angle π 2 and then clockwise by angle π 3 . 5. Do the following three points determine a triangle or not? If so, find the angles and length of each side of the triangle. (a)

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Unformatted text preview: P 1 = 1 2 , P 2 = 2 1 , P 3 = -1-1 . (b) P 1 = 1 , P 2 = 2 1 , P 3 = 3 2 . 1 (c) P 1 = 1 2 1 , P 2 = 3 1 , P 3 = 3 1 . (d) P 1 = 1 1 , P 2 = 1 1 , P 3 = 1 1 . 6. Find the range of a , if possible, such that both eigenvalues of following matrices have negative real parts ( a ) a 1 2 a ( b ) 1 a 2 1 ( c ) 1 a-1 2...
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