MATH-205 Midterm: Bates MATH 205 021502johnson205examsolns
Document Summary
Answer key for exam #1: the vectors. 1 each have have length 6: p32 + 02 + 42 + 12 + +12 + 32 = 6 = p12 + 12 + 12 + 42 + 42 + 12. Their dot product is 3 + 0 + 4 + 4 + 4 + 3 = 18, so the angle between them satis es cos = 2: we use elimination on an augmented matrix. First two steps: subtract twice the rst row from the second, and three times the rst row from the third. Next two steps: multiply the second row by 1, and then add. Ve times the second row to the third. Then the second equation becomes x2 + 15 = 13, so x2 = 2. Rst equation becomes x1 4 + 9 = 10, so x1 = 5: the inverse of 2 3. 3 4 is and the inverse of 3 4.
