Chemical Engineering Hand Written_Notes_Part_27

Chemical Engineering Hand Written_Notes_Part_27 - 56 3....

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

View Full Document Right Arrow Icon
56 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES Figure 1 the following system of equations (1.7) " 2 1 1 1 # x = " 1 5 # There are two ways of interpreting the above matrix vector equation geometri- cally. Row picture : If we consider two equations separately as (1.8) 2 x y = " 2 1 # T " x y # =1 (1.9) x + y = " 1 1 # T " x y # =5 then, each one is a line in x-y plane and solving this set of equations simultaneously can be interpreted as f nding the point of their intersec- tion (see Figure 1 (a)). Column picture : We can interpret the equation as linear combina- tion of column vectors, i.e. as vector addition (1.10) x 1 " 2 1 # + x 2 " 1 1 # = " 1 5 # Thus, the system of simultaneous equations can be looked upon as one vector equation i.e. addition or linear combination of two vectors (see Figure 1 (b)).
Background image of page 1

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

View Full DocumentRight Arrow Icon
1. SOLUTION OF Ax = b AND FUNDAMENTAL SPACES OF A 57 Now consider the following set of equations (1.11) " 1 2 1 2 #" x 1 x 2 # = " 2 5 # In row picture, this is clearly an inconsistent case(
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

Page1 / 2

Chemical Engineering Hand Written_Notes_Part_27 - 56 3....

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