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# hw7 - Winter 2011 Math 67 Linear Algebra Homework 7 Problem...

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Winter 2011 Math 67 Linear Algebra Homework 7 Problem A. (this is Artin 1.3.1) Compute the following determinants: 1 i 2 - i 3 (1) 1 1 1 - 1 (2) 2 0 1 0 1 0 1 0 2 (3) 1 0 0 0 5 2 0 0 8 6 3 0 0 9 7 4 (4) 1 4 1 3 2 3 5 0 4 1 0 0 2 0 0 0 (5) Problem B. (this is Artin 1.3.8) Let A be an n -by- n matrix. What is det( - A )? (You do not need to hand this in.) Problem C. Let P and Q be matrices of size n -by- n and m -by- m . Form a new matrix of the form P 0 0 Q This matrix has dimensions ( n + m )-by-( n + m ). Prove that det P 0 0 Q = (det P )(det Q ) using the definition of the determinant. Do any example where n = m = 2, but do not hand this part in. Problem D. Compute the eigenvalues of the matrix in A(5), above. (Use a

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hw7 - Winter 2011 Math 67 Linear Algebra Homework 7 Problem...

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