Question

Let $M_1 = egin{bmatrix} -1 & -1 \ -1 & -1 end{bmatrix}$ and $M_2 = egin{bmatrix} 3 & 1 \ 1 & 2 end{bmatrix}$. Consider the inner product $langle A, B angle = ext{trace}(A^T B)$ in the vector space $mathbb{R}^{2 imes 2}$ of $2 imes 2$ matrices. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of $mathbb{R}^{2 imes 2}$ spanned by the matrices $M_1$ and $M_2$. $left{ egin{bmatrix} -1/2 & -1/2 \ -1/2 & -1/2 end{bmatrix}, egin{bmatrix} & \ & end{bmatrix} ight}$

          Let $M_1 = egin{bmatrix} -1 & -1 \ -1 & -1 end{bmatrix}$ and $M_2 = egin{bmatrix} 3 & 1 \ 1 & 2 end{bmatrix}$. Consider the inner product $langle A, B 
angle = 	ext{trace}(A^T B)$ in the vector space $mathbb{R}^{2 	imes 2}$ of $2 	imes 2$ matrices. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of $mathbb{R}^{2 	imes 2}$ spanned by the matrices $M_1$ and $M_2$. $left{ egin{bmatrix} -1/2 & -1/2 \ -1/2 & -1/2 end{bmatrix}, egin{bmatrix} & \ & end{bmatrix} 
ight}$

Let M1 = eginbmatrix -1 -1 -1 -1 endbmatrix and M2 = eginbmatrix 3 1 1 2 endbmatrix. Consider the inner product langle A, B
angle = exttrace(A^T B) in the vector space mathbbR^2 imes 2 of 2 imes 2 matrices. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of mathbbR^2 imes 2 spanned by the matrices M1 and M2. left eginbmatrix -1/2 -1/2 -1/2 -1/2 endbmatrix, eginbmatrix endbmatrix
ight

Added by Amy L.

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