Example SVP4 leaves several details for the reader to check. Verify these five claims.
The five claims from Example SVP4 are:
(1) {3x2−5x−2,2x2−7x+6,x3−2x2+x−2} is a subset of W.
(2) {3x2−5x−2,2x2−7x+6,x3−2x2+x−2} is linearly independent.
(3) {3x2−5x−2,2x2−7x+6,x3−2x2+x−2,−x4+2x3+5x2−10x,x4−16} is a subset of W.
(4) {x−2,x2−2x,x3−2x2,x4−2x3} is a subset of W.
(5) {x−2,x2−2x,x3−2x2,x4−2x3} is linearly independent.