Math 1553 quiz 6: chapter 3 (10 points, 10 minutes) Solutions: suppose a is a 3 3 matrix with det(a) = 1, and let t : r3 r3 be the transfor- mation t (x) = ax. 0 1 = 1, so a is not necessarily i3. If det(a) = 1 then det( a) = ( 1)3 det(a) = ( 1)( 1) = 1, so (b) is true. If b is any 3 3 matrix, then det(ab) = det(a) det(b) = det(b), so (c) is true. If vol(s) = 10 then vol(t (s)) = | det(a)| vol(s) = 1 10 = 10, so (d) is true. 4: suppose det a b c g h i = 2. 3a + d 3b + e 3c + f g 4a h 4b f i 4c. e.
