Exercise 1.3.26

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In $\mathrm{M}_{m 	imes n}(F)$ define $\mathrm{W}_{1}=\left\{A \in \mathrm{M}_{m 	imes n}(F): A_{i j}=0ight.$ whenever $\left.i>jight\}$ and $\mathrm{W}_{2}=\left\{A \in \mathrm{M}_{m 	imes n}(F): A_{i j}=0ight.$ whenever $\left.i \leq jight\} . \quad\left(\mathrm{W}_{1}ight.$ is the set of all upper triangular matrices as defined on page 19.) Show that $\mathrm{M}_{m 	imes n}(F)=\mathrm{W}_{1} \oplus \mathrm{W}_{2}$.

Jephian C.-H. Lin · Accepted Answer

This is similar to \href{./exercise_1-3-24}{Exercise 1.3.24}.

Exercise 1.3.26

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Exercise 1.3.26

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