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hwB12 - x(2 and x(3 are the solutions obtained above for b...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 12 Due Fri 02/29 Solve by hand without using calculator matrix functions. Show all intermediate steps. Let A = 1 4 4 4 2 2 0 2 1 1 3 3 1 3 1 2 (i) (8 pts.) Obtain the LU factorization A = LU . (ii) (12 pts.) Determine A - 1 by solving LY = I followed by UX = Y , where Y and X are 4 × 4 matrices of unknowns. Solved Examples S 12.1 . (i) Solve Ax = b , where A = 2 - 4 2 - 1 5 2 1 - 1 3 and b = e (1) = 1 0 0 (ii) From your work in part (i) , obtain the LU factorization of A . (iii) Using the above factorizations, solve Ax = b for b equal to the other two unit vectors, namely e (2) and e (3) . (iv) If x (1)
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Unformatted text preview: , x (2) and x (3) are the solutions obtained above for b = e (1) , e (2) and e (3) , respectively, what is the relationship of the matrix X = £ x (1) x (2) x (3) / to A ? Brieﬂy explain how x (2) and x (3) can be obtained at the same time as x (1) . S 12.2 . (i) Determine the LU factorization of A = 2 7-7-3 1 5-5-3 2 3 1 3 1 4-2 2 (ii) Solve Ax = b , where b = [10 5-6 3] T , by means of the two triangular systems Ly = b and Ux = y...
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