# Monthly Archives: May 2011

## Linear Algebra and Its Applications, Exercise 1.6.18

Exercise 1.6.18. Suppose that Show that Answer: We have The product of two upper triangular matrices is also an upper triangular matrix, and multiplying by a diagonal matrix preserves this. The left side of the final equation above is therefore … Continue reading

## Linear Alegbra and Its Applications, Exercise 1.6.17

Exercise 1.6.17. (a) Suppose that the n by n matrix A can be factored as LDU, where L and U have ones on the diagonal. Factor the transpose of A. (b) If we have what triangular systems will provide a … Continue reading

## Linear Algebra and Its Applications, Exercise 1.6.16

Exercise 1.6.16. (i) If A is an n by n symmetric matrix, how many entries of A can be chosen independently of each other? (ii) If If K is an n by n skew-symmetric matrix, how many entries of K … Continue reading

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## Linear Algebra and Its Applications, Exercise 1.16.15

Exercise 1.6.15. For any square matrix B and matrices A and K where prove that A is symmetric and K is skew-symmetric, i.e., For the case where compute A and K and show that B can be expressed as the … Continue reading

## Linear Algebra and Its Applications, Exercise 1.6.14

Exercise 1.6.14. For any m x n matrix A, prove that and are symmetric matrices. Provide an example where these matrices are not equal. Answer: Per Equation 1M(i) on page 47 we have Substituting for B we have Since is … Continue reading