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Exercise 1.6.30

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It can be checked that $W_{1}$ and $W_{2}$ are subspaces with dimension $3$ and $2$ . We also can find out that $W_{1} \cap W_{2} = {(\begin{matrix} 0 & a \\ - a & 0 \end{matrix}) \in V : a, b \in 𝔽}$ and it has dimension $1$ . By the formula of the previous exercise, we have that dimension of $W_{1} + W_{2}$ is $2 + 3 - 1 = 4$ .

jephianlin

2011-06-27 00:00

Exercise 1.6.30

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