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Introduction to Linear Algebra

Exercise 3.1.30

Answers

(a): If $u$ and $v$ are both in $S + T$ , then $u = s_{1} + t_{1}$ and $v = s_{2} + t_{2}$ . So $u + v =$ $(s_{1} + s_{2}) + (t_{1} + t_{2})$ is also in $S + T$ . And so is $c u = c s_{1} + c t_{1} : S + T =$ subspace.
(b): If $S$ and $T$ are different lines, then $S \cup T$ is just the two lines (not a subspace) but $S + T$ is the whole plane that they span.

mathchakra

2022-01-16 13:28

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