This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: solution(s). 5. (a) (8 points) If T : R 3 → R 3 is a linear transformation that satisﬁes T 1 1 1 = 12 and T 1 = 5 5 , ﬁnd the values T 3 3 3 = ? and T 3 3 4 = ? (b) (7 points) Let a transformation T : R 3 → R 3 be deﬁned by T x y z = 2 y + z x + y . Find a 3 × 3 matrix M such that T ( u ) = Mu for any vector u ∈ R 3 . 6. (15 points) For each of the following pairs of matrices M,N , compute the matrix products MN , or specify if the product does not make sense given the dimensions of M and N . (a) M = ± 1 0 0 2 ² , N = ± 1 3 5 7 9 11 ² (b) M = ± 1 1 x111 ² , N = a b c 2 (c) M = 1 2 3 4 5 6 7 8 9 , N = 0 0 3 0 2 0 1 0 1 (d) M = ± x y ² , N = ( 20 10 ) (e) M = ± 1 3 5 7 9 11 ² , N = ± 1 3 5 7 9 11 ² 3...
View
Full
Document
This note was uploaded on 11/13/2011 for the course MATH 22a taught by Professor Chuchel during the Winter '08 term at UC Davis.
 Winter '08
 chuchel
 Linear Algebra, Algebra, Approximation

Click to edit the document details