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Two vector spaces V and W over the same field F are isomorphic if there is a bisection$\mathit{T}\mathbf{:}\mathit{V}\mathbf{鈫�}\mathit{W}$ which preserves addition and scalar multiplication, that is, for all vectors u and v in V, and all scalars$\mathit{C}\mathbf{鈭�}\mathit{F}\mathbf{,}\mathit{T}\left(u+v\right)\mathbf{=}\mathit{T}\left(u\right)\mathbf{+}\mathit{T}\left(v\right)$ and$\mathit{T}\left(cv\right)\mathbf{=}\mathit{c}\mathit{T}\left(v\right)$.The correspondence T is called an isomorphism of vector spaces.

When$T:V鈫�W$ is an isomorphism, then $T:V\text{'}鈫�W$ it鈥檚 emphasize that it is an isomorphism When V and W are isomorphic, but the specific isomorphism is not named, we鈥檒l just write $V饾啅=W$.

Let $T:V鈫�W$ be a linear transformation with Ker$\left(T\right)=\left\{0\right\}$. If V and W are of the same dimensionality, then, T will be an isomorphism.

Since, we have transformation between two same spaces, the dimension will be equal,

$dim{p}_4=5$, and we know that $ker\left(T\right)=\left\{0\right\}$. By using the theorem, so, T will be an isomorphism.

Hence, the statement is true.