MATH-205 Midterm: Bates MATH 205 100801johnson205examsolns

• School: Bates College
• Department: Mathematics
• Course: MATH-205
• Professor: All

Document Summary

Answer key for exam #1: the vectors . 1 have lengths p12 + 12 + 12 + 12 = 2 and p12 + 12 + 02 + 12 = 3, 2 3 respectively, and their dot product is 1 + 1 + 0 + 1 = 3. So the angle between them satis es cos = 6 , or 30 : we use elimination on an augmented matrix. Subtracting the rst row from the second and third, and then adding the second row to the third, we have. The last step wasn"t necessary since the system was already triangular, but it doesn"t hurt. The second equation gives x3 = 4 and the third one says x2 = 2. Then the rst equation becomes x1 + 2 + 8 = 3, so x1 = 7: here we have to reduce [a i] to i a 1 by row operations.