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# hw06 - Ux = y solve Ly = b Using the solution y solve Ux =...

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ENEE 241 02* HOMEWORK ASSIGNMENT 6 Due Thu 02/26 Solve by hand without using your calculator. Show all intermediate steps. Let L = 1 0 0 0 - 3 1 0 0 3 - 3 1 0 5 3 - 3 1 (i) (4 pts.) Solve Lx = b for arbitrary x and b . Display L - 1 . (ii) (5 pts.) Express the matrix G = 5 6 - 3 - 2 3 - 6 1 0 - 3 2 0 0 1 0 0 0 in the form G = PLD , where D is a diagonal matrix, P is a permutation matrix and L is as given above. Determine G - 1 . (iii) (5 pts.) Show that the matrix A = 2 1 1 - 3 - 6 - 5 - 2 8 6 9 - 1 - 2 10 - 1 11 - 29 can be expressed in the form A = LU where U is an upper triangular matrix and L is as above. What is U ? ( Hint : You know L - 1 from part (i).) (iv) (6 pts.) Solve the equation Ax = b for b = £ - 1 4 6 3 / T as follows. Letting
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Unformatted text preview: 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.) Solved Example S 6.1 . 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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