Exercise 1.2.16

Question

Let $\mathrm{V}$ denote the set of all $m 	imes n$ matrices with real entries; so $\mathrm{V}$ is a vector space over $R$ by Example 2. Let $F$ be the field of rational numbers. Is $\mathrm{V}$ a vector space over $F$ with the usual definitions of matrix addition and scalar multiplication?

Jephian C.-H. Lin · Accepted Answer

Yes. All the condition are preserved when the field is the rational numbers.

Exercise 1.2.16

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Exercise 1.2.16

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