Let $$M_1 = \left[\begin{array}{cc} -1 &1\cr -1 &1 \end{array}\right] \ \mbox{ and } \ M_2 = \left[\begin{array}{cc} 6 &-1\cr 1 &0 \end{array}\right].$$ Consider the inner product $\langle A,B\rangle ={\rm trace} (A^T B)$ in the vector space ${\mathbb R}^{2\times 2}$ of $2\times 2$ matrices. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of ${\mathbb R}^{2\times 2}$ spanned by the matrices $M_1$ and $M_2$.

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