MidtermMath2JWinter11_solutions

MidtermMath2JWinter11_solutions - Math 2J, Winter 11...

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Unformatted text preview: Math 2J, Winter 11 Instructor : Yunho Kim The Midterm Exam Date : Feb. 7th UID Name Class Lec. A, 1:00pm - 1:50pm Number Score 1. a) b) 2. 3. a) b) 4. 5. a) b) Total Score / 100 1 Problem 1. Solve the following systems. a. (15pts) 2 x 1 3 x 2 = 1 x 1 + 6 x 2 = 4 Solution. x 1 = 2 ,x 1 = 1 . b. (15pts) 3 x 1 + x 2 2 x 3 = 4 x 1 + 3 x 2 4 x 3 = 1 2 x 1 x 2 + 2 x 3 = 1 Solution. x 1 = 1 , x 2 = 0 , x 3 = 1 / 2 . 2 Problem 2. (15pts) Find the LU factorization (or decomposition) of the following matrix A = 1 4 3-1-3 3 6 1 , that is, find a lower triangle matrix L and an upper triangular matrix U such that A = LU . (Hint : You have to apply only row operations of type III.) You dont need to find an explicit form of the matrix L . It is enough to find elementary matrices which are factors of L with correct order of multiplication. What is det ( A ) ? (Hint : If you know the LU factorization of A , then it will be extremely easy to compute the determinant. Otherwise, you should compute the determinant ofextremely easy to compute the determinant....
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MidtermMath2JWinter11_solutions - Math 2J, Winter 11...

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