hw07 - 3 and b = e (1) = 1 (ii) From your work in part (i)...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 7 Due Thu 03/05 Solve by hand without using calculator matrix functions. Show all intermediate steps. Let A = 2 4 - 2 2 - 1 1 4 - 7 1 3 1 - 3 3 8 1 - 6 (i) (8 pts.) Solve Ax = b , where b is the standard unit vector [ 1 0 0 0 ] T . (ii) (12 pts.) Using the multipliers obtained in the forward elimination phase, along with the resulting matrix U , solve Ax = b when b equals each of the remaining three standard unit vectors. Hence display A - 1 . Solved Examples Note: These examples make mention of the LU factorization of a matrix, obtained by Gaussian elimination. The lower triangular matrix is formed used the multipliers obtained in the forward elimination phase, by placing them below the leading diagonal of an identity matrix after reversing their signs. S 7.1 . (i) Solve Ax = b , where A = 2 - 4 2 - 1 5 2 1 - 1
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Unformatted text preview: 3 and b = e (1) = 1 (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) , 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 = b x (1) x (2) x (3) B to A ? Briey explain how x (2) and x (3) can be obtained at the same time as x (1) . S 7.2 . (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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