MAT-2240 Midterm: MATH 2240 App State summer2006 Exam1 answer key
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Math 250 section b1 summer 2006: (10pts): find the general solution for the following system of equations using gaussian elimination. + x4 5x5 = 4 x1 + x2 + x3 + x4 2x5 = 4. First, we translate the system into an augmented matrix. Now we can read o the general solution: x1 = 1 x2 + 2x5 x2 is free x3 = 1 x4 = 2 x5 is free. A0 rotates a vector zero degrees that is the vector is left unchanged: a0~v = ~v. A0 = i2 (the identity matrix). (b) argue that a (a ~v) = a + ~v for all ~v r2. sin( ) sin( ) sin( ) Let"s prove this two ways: a rotates ~v by an angle of . Then a rotates a ~v by an angle of . Thus a (a ~v) is ~v rotated by an angle of + .
