Question

$R^2$is a subspace of$R^3.$

Short answer

The above statement is false.

$R^2$is not a subspace of$R^3$

Step-by-step solution

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. $W\subset V.$

To find whether R2 is a subspace of R3 or not

Let us take an arbitrary element$\left(a,b\right)\in R^2.$

Since the element in $R^3$ is of type (a, b, c).

$\Rightarrow (a,b)\notin R^3$

$\Rightarrow R^2\not\subset R^3$

Hence, $R^2$is not a subspace of$R^3$

Final Answer

Since $R^2$is not a subset of$R^3,$ hence, $R^2$is not a subspace of$R^3.$