hwB10 - G = DPL , where D is a diagonal matrix, P is a...

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ENEE 241 02* HOMEWORK ASSIGNMENT 10 Due Fri 02/22 Solve by hand without using calculator matrix functions. Show all intermediate steps. Let U = 1 - 2 1 0 0 1 - 2 1 0 0 1 - 2 0 0 0 1 (i) (4 pts.) Solve Ux = b for arbitrary x and b . Display U - 1 . (ii) (6 pts.) Show that the matrix A = 1 - 2 1 0 - 2 5 - 4 1 1 - 4 6 - 4 0 1 - 4 6 can be expressed in the form A = LU where L is a lower triangular matrix and U is as above. Also, determine L . ( Hint : You know U - 1 from part (i) .) (iii) (5 pts.) Solve the equation Ax = b for b = £ 1 2 - 2 - 1 / T as follows. Letting Ux = y , solve Ly = b . Using the solution y , solve Ux = y for x . (Since b is in numerical form, it is not necessary to use L - 1 or U - 1 here.) (iv) (5 pts.) Express the matrix G = 0 4 - 8 4 3 - 6 3 0 - 4 2 0 0 1 0 0 0 in the form
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Unformatted text preview: G = DPL , where D is a diagonal matrix, P is a permutation matrix and L is computed as in part (ii) . Using this form and the result of part (i) , determine G-1 . Solved Example S 10.1 . The matrix A can be factored as A = LU , where L = 1 2 1 3 4 1-1-3 1 1 and U = 1 1 3-1-1-5 3 13-26 (i) Obtain the matrix A . (ii) Solve Ax = b , where 4 1-3 4 / T , by means of the two triangular systems of equations Ly = b and Ux = y...
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This note was uploaded on 03/21/2010 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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