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HP2_S04_ChE_252 - 4 Bonus question In a mailroom the...

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Department of Chemical Engineering University of California, Santa Barbara Ch.E. 252 Due: April 14, 2004 Home Problem 2 1. Consider a linear equation, y = Ax . What condition must the n x n matrix A satisfy in order that y and x have the same length (i.e., Euclidean norm) for any arbitrary x 0 ? Justify your answer. 2. Again, consider the linear equation, y = Ax , where A is n x n . Prove that the eigenvalues of A 2 are { λ ι 2 }, where λ ι is an eigenvalue of A . 3. Derive analytical expressions for the singular values of a 2 x 2 matrix.
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Unformatted text preview: 4. ( Bonus question ) In a mailroom, the contents of four packages are spilled onto the floor. All four packages are the same size, but each has a different mailing label and originally each contained a different object. If a person later discovers the spill, what is the probability that exactly three objects will be placed in their correct packages?...
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