**Unformatted text preview: **11/11/2001 SUN 12:18 FAX 6434330 MOFFITT LIBRARY .001 P. Vojta Math 54M First Midterm Spring 2001
80 mimcl'QS [This was a fairly easy exam: median was 45 out of a possible 50.] 1. (7 points) Compute (or, if it is not deﬁned, say so):
1 (a). [g g g] 31 10 . .1 0 1 _ 2
(b).A B,WhereA—[1 0 andB— 3 . 121
212—
771
12 43 —104
[341-4121111211 (e). The distance between (9, 4, 7, 2, 0) and (6, 2,8, 0, 1) in R5.
(f). u - v, Where u = (9, 4, 7, 2, 0) and v = (1, —2, 3, 2, 8) DONH 2. (7 points) Solve the system: w+3y+z+u—v=0
2y+3z—4u+3v:3
2n+v=3 'u = 2
U .I. —2
3. (10 points) Invert the matrix 1 3 —4 .
*3 *7 10 4. (6 points) State the deﬁnition of an invertible matrix, and give three conditions that are
equivalent to invertibiiity. 5. (5 points) Find the projection of (1, 1, 0) on (2, 1, —2).
6. (5 points) Is Z (= the set of all integers) a subspace of R — R1? Justify your answer. 7. (10 points) Are the vectors
(1,0, 0), (2, 4, 7) (7, 3, 5) linearly independent? Justify your answer. ...

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