a Show that the linear system 2xy5 x2y2 xy3 is inconsistent

a) Show that the linear system:

2x-y=5

-x+2y=2

x+y=-3

is inconsistent.

b) Use the orthogonal projection of a vector on a subspace to find the best approximation of a solution of the linear system in a) (Show work)

c) Find a best approximation of the linear equation in a) using normal equations.

a) The System of equations have no solutions then they are called inconsistent

Given that 2x-y=5---->1

-x+2y=2--->2

x+y=-3---->3

from 1 and 2

2+3=> (-x+2y)+(x+y)=-1

=>3y=-1

=>y=-1/3

from 3-------->x+y=-3

x+(-1/3)=-3

=>x=-3+(1/3)=-8/3

So x= -8/3 and y = -1/3

Now, from 1, 2(-8/3)-(-1/3)=(-16/3)+(1/3)=-15/3=-5

from 2, -(-8/3)+2(-1/3)=8/3-(2/3)=6/3=2

from 3, -8/3+(-1/3)=-9/3=-3

therefore the system of equations have no solution.

therefore they are inconsistent.