Linear projection/Description with matrix/Exercise

Let ${}\varphi \colon V\rightarrow V$ denote a linear projection on a finite-dimensional ${}K$-vector space ${}V$. Show that ${}\varphi$ is described, with respect to a suitable basis ${}v_{1},\ldots ,v_{n}$ of ${}V$, by a matrix of the form

${\begin{pmatrix}1&0&\cdots &\cdots &\cdots &0\\0&\ddots &\ddots &\ddots &\vdots &\vdots \\\vdots &\ddots &1&\ddots &\ddots &\vdots \\\vdots &\ddots &\ddots &0&\ddots &\vdots \\\vdots &\vdots &\ddots &\ddots &\ddots &0\\0&\cdots &\cdots &\cdots &0&0\end{pmatrix}}.$

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