91影视

Linearly independent is defined as the property of a set having no linear combination of its elements equal to zero when the coefficients are taken from a given set unless the coefficient of each element is zero.

The vectors in the kernel of an $n脳m$ matrix A correspond to the linear relations among the column vectors role="math" localid="1659352322874" $\stackrel{鈫�}{v_1},.....,\stackrel{鈫�}{v_m}$.of A: The equation

$A\stackrel{鈫�}{x}=\stackrel{鈫�}{0}$means that $x_1\stackrel{鈫�}{v_1}+...+x_m\stackrel{鈫�}{v_m}=\stackrel{鈫�}{0}$.

In particular, the column vectors of A are linearly independent if (and only if) $\mathrm{ke}r\left(A\right)=\left\{\stackrel{鈫�}{0}\right\}$,or, equivalently, if$rank\left(A\right)=m$. This condition implies that $m鈮�n$.

Thus we can find at most linearly independent vectors in ${\mathrm{鈩�}}^n$.

The columns vectors are independent$鈬�$ the rank of Ais$3\left(3鈮�4\right)$

So,$rref$

$\left(A\right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]$