1) prove that for any five vectors (x1, ..., x5) in R3 there exist real numbers (c1, ..., c5), not all zero, so that BOTH
c1x1+c2x2+c3x3+c4x4+c5x5=0 AND c1+c2+c3+c4+c5=0
2)Let T:R5-->R5 be a linear transformation and x1, x2 & x3 be three non-zero vectors in R5 so that
T(x1)=x1...