(线代证明)已知α1,α2,α3线性无关,α4可由α1,α2,α3线性表出,且表...答:α4=k1α1+k2α2+k3α3 任意三个向量 case 1: α1,α2,α3 α1,α2,α3线性无关 ( given )case 2: α1,α2,α4 m1α1+m2α2+m3α4=0 m1α1+m2α2+m3(k1α1+k2α2+k3α3)=0 (m1+m3k1)α1+(m2+m3k2)α2+(m3k3)α3=0 => m1+m3k1=0 (1)m2+m3k2=0...
线性代数题已知a1, a2 ,,,an, b线性无关 证明a1+b ,a2+b,,,an+b也...答:证:设 r1(a1+b)+r2(a2+b)+...+rn(an+b) = 0 那么 r1*a1+r2*a2+...+rn*an+(r1+r2+...+rn)*b = 0 因为 a1,a2,...,an,b 线性无关,所以 r1=r2=r3=...=rn=(r1+r2+...+rn)=0,特别地,r1=r2=r3=...=rn=0 ,所以 a1+b,a2+b,...,an+b 也线性无关。...