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Chapter 3: Q31E (page 164)

R2is a subspace ofR3.

Short Answer

Expert verified

The above statement is false.

R2is not a subspace ofR3

Step by step solution

01

Necessary condition

The necessary condition for a set W to be a subspace of a vector space V over F is that the set W must be the subset of vector space V.

i.e. W鈯�V.

02

To find whether R2 is a subspace of R3 or not

Let us take an arbitrary elementa,b鈭�R2.

Since the element in R3 is of type (a, b, c).

鈬�(a,b)鈭�R3

鈬�R2鈯�R3

Hence, R2is not a subspace ofR3

03

Final Answer

Since R2is not a subset ofR3, hence, R2is not a subspace ofR3.

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