MATH347DS L02: Linear Mappings 

octave] 
ex=[1; 0]; ey=[0; 1];
 
octave] 
b=[0.2; 0.4]; I=[ex ey]; I*b

ans =

0.20000

0.40000 

octave] 
th=pi/6; c=cos(th); s=sin(th);
 
octave] 
tvec=[c; s]; nvec=[-s; c];
 
octave] 
A=[tvec nvec];
 
octave] 
x=A\b

x =

0.37321

0.24641 

octave] 
[x(1)*tvec x(2)*nvec]

ans =

0.32321 -0.12321

0.18660 0.21340 

octave]

Figure 1. Alternative decompositions of force on inclined plane.