MATH 240 Midterm: MATH 240 NIU Exam1 sample
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Show all of the work necessary to justify your answers: (15 pts) (a) use gauss-jordan reduction to solve the following linear system. x1 +2x2 +3x3 = 3x1 +x2 x3 = 2 (b) explain why the answer to part (a) shows how to write the vector b = . As a linear combination of the vectors v1 = . , v2 = : (10 pts) find the inverse of the matrix a = . , and v3 = : (15 pts) write the matrix a = (cid:20) 1 2. 2 1 (cid:21) as a product of elementary matrices. Then write a 1 as a product of elementary matrices. (hint: you can do this without nding a 1. : (15 pts) show that if a is a nonsingular matrix and ab = ac for matrices b, c, then. Check each of these laws: (1) commutative law for addition, (2) associative law for addition, and (5), (6) distributive laws.
