lecture_8

lecture_8 - MA 35100 LECTURE NOTES: FRIDAY, JANUARY 29...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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

Page1 / 2

lecture_8 - MA 35100 LECTURE NOTES: FRIDAY, JANUARY 29...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online