线性相关证明题If η is a solution of AX=b ,which and R(A)=r.Letζ1ζ2ζ3ζ4ζ5 be a basis of the solution space of AX=0.Show η ζ1ζ2ζ3ζ4ζ5 that are linearly independent.

来源：学生作业帮助网编辑：作业帮时间：2024/11/17 01:55:18

线性相关证明题If η is a solution of AX=b ,which and R(A)=r.Letζ1ζ2ζ3ζ4ζ5 be a basis of the solution space of AX=0.Show η ζ1ζ2ζ3ζ4ζ5 that are linearly independent.
线性相关证明题
If η is a solution of AX=b ,which and R(A)=r.
Letζ1ζ2ζ3ζ4ζ5 be a basis of the solution space of AX=0.
Show η ζ1ζ2ζ3ζ4ζ5 that are linearly independent.

线性相关证明题If η is a solution of AX=b ,which and R(A)=r.Letζ1ζ2ζ3ζ4ζ5 be a basis of the solution space of AX=0.Show η ζ1ζ2ζ3ζ4ζ5 that are linearly independent.
Suppose η,ζ1,ζ2,ζ3,ζ4,ζ5 are linearly dependent.
Then there are k1,k2,...,k6 of which not all are 0 such that k1η+k2ζ1+k3ζ2+k4ζ3+k5ζ4+k6ζ5=0.
So A(k1η+k2ζ1+k3ζ2+k4ζ3+k5ζ4+k6ζ5)=0.
Because Aη=b,Aζi=0.
So k1b=0,namely k1=0.
So k2ζ1+k3ζ2+k4ζ3+k5ζ4+k6ζ5=0.
Because ζ1,ζ2,ζ3,ζ4,ζ5 are a basis of the solution space of AX=0,
so they are linearly independent.
So k2=k3=...=k6=0
That is impossible.
So η,ζ1,ζ2,ζ3,ζ4,ζ5 are linearly independent

线性相关证明题If η is a solution of AX=b ,which and R(A)=r.Letζ1ζ2ζ3ζ4ζ5 be a basis of the solution space of AX=0.Show η ζ1ζ2ζ3ζ4ζ5 that are linearly independent. 线性相关,向量,证明,6题, 大一线性代数证明线性相关线性相关问题.求证明线性代数证明线性相关题设n维向量a1,a2,a3 线性相关,a2,a3,a4 线性无关,试证明a1 可以由a2,a3 线性表示. 向量组A线性相关,则其中的任一部分组都线性相关,为什么不对?求证明, 线性相关,第四题, 线性相关和线性无关（证明题）设向量组R={a1,a2,a3}可由向量组S={b1,b2}线性表出.证明:R是线性相关向量组.书上是这样写的,有点不懂的地方：考虑线性组合：x1a1+x2a2+x3a3 由已知,可设a1=a11b1+a21b2,a 线性代数,如果向量组a与向量组b线性相关,又与向量组c线性相关,b与c是否相关,求证明, 证明向量组a,b,c 线性相关,则向量组-2a,3b,-1/2c 线性无关一道关于向量线性相关的证明题若向量a1,a2线性相关,向量b1,b2线性相关,问a1+b1与a2+b2是否一定线性相关? 线性代数证明题：设向量组a1、a2,.,a(m-1) (m大于等于3)线性相关,向量组a2,.,am线性无关,求am能由a2,…,am-1线性表示设向量组[a,b]线性无关,且向量组[a+c,b+c]线性相关,证明向量c可由[a,b]线性表出向量组A线性相关,A=0?线性不相关,A不等于0?如题线性代数,线性相关证明题,证明：两个n（n>0）维向量线性相关的充分必要条件是两个向量对应分量成比例. 证明：若a1a2a3向量线性相关,a2a3a4线性无关,证明a1能由a2a3线性表示线性代数证明题：设向量组a1、a2,.,a(m-1) (m大于等于3)线性相关,向量组a2,.,线性无关证明：（1）a1能由a2,a3,.a(m-1)线性表示（2）a1不能由a2,a3,.a(m-1)线性表示线性相关证明B怎么证明的啊