# Find a basis for the space of 2 times 2 diagonal matrices. text{Basis }=left{begin{bmatrix}&& end{bmatrix},begin{bmatrix}&& end{bmatrix}right}

Find a basis for the space of $2×2$ diagonal matrices.
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Jayden-James Duffy
Step 1
let the space of $2×2$ diagonal matrices be as
$\left[\begin{array}{cc}a& 0\\ 0& b\end{array}\right]$
we can choose values of a and b randomly Step 2
Basis of matrix $\left[\begin{array}{cc}a& 0\\ 0& b\end{array}\right]$ can be taken as
a=1,b=0
$\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$
a=0, b=1 $\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]$