W \(\displaystyle{ K ^{n}}\)
\(\displaystyle{ U=span(u _{1} , ...,u _{k})}\) oraz \(\displaystyle{ W=span(w _{1} , ...,w_{l})}\)
Niech \(\displaystyle{ M=\left[ u _{1}, ..., u _{k}, w _{1},...,w _{l} \right] \in K ^{n, k+l}}\)
Pokaż, że:
1) \(\displaystyle{ rankM=dim\left( U+W\right)}\)
2) \(\displaystyle{ dim\left( kerM\right) \ge dim\left( U \cap W\right)}\)