This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MA 35100 LECTURE NOTES: FRIDAY, JANUARY 29 Matrix of a Linear Transformation In the previous lecture, we saw that given a system of n equations in m unknowns, we could express it in the form A~x = ~ b in terms of an n × m matrix A and vectors ~x ∈ R m and ~ b ∈ R n . Similarly, a linear transformation T : R m → R n can be expressed in the form T ( ~x ) = A~x in terms of an n × m matrix and vector ~x ∈ R m . Hence, a system of equations can be expressed as a linear transformation, where T ( ~x ) = ~ b . Conversely, say that we have a linear transformation T : R m → R n . We will discuss how to find the n × m matrix A . First we begin with an example to gain some intuition. Say that we have the transformation T : R 3 → R 3 given by T ( ~x ) = A~x in terms of the 3 × 3 matrix A = 1 2 3 4 5 6 7 8 9 . We want to compute T 1 , T 1 , and T 1 . To do so, write A = ~v 1 ~v 2 ~v 3 in terms of the columns of A . By definition we have the product A~x = x 1 ~v 1 + x 2...
View
Full
Document
This note was uploaded on 10/18/2010 for the course MATH 351 taught by Professor Egoins during the Spring '10 term at Purdue.
 Spring '10
 EGoins
 Linear Algebra, Algebra, Equations, Vectors

Click to edit the document details