设X1,X2,X3线性无关,证X1,X2,X3与X1+X2,X1-X2,X1+X3,X1-X3等价

(x1+x2,x1-x2,x1+x3,x1-x3)=(x1,x2,x3)KK =1 1 1 11 -1 0 00 0 1 -1由于x1,x2,x3线性无关所以 r(x1+x2,x1-x2,x1+x3,x1-x3)=r(K)=3所以 r(x1+x2,x1-x2,x1+x3,x1-x3)=3=r(x1,x2,x3)再由 x1+x2,x1-x2,x1+x3,x1-x3可由x1...