Let A= [1 -2 -3 0
0 1 0 -1
1 -1 1 0]
and K={(x,y,z,w) E R^4: Av^t =0}
Prove that K is a subspace of R^4. Hint: use a matrix equation rather than 3 linear equations.
Any help is greatly appreciated!!
See Linear subspace. is a subspace because these three conditions hold:
To show is a subspace, you must show the three conditions listed in the linear subspace link hold.
The first condition, for example, is To show this holds, you note as I did that so the vector satisfies the equation defining , which is . Notice the hint says use a matrix equation.
The other two conditions are done similarly.