Let M be a 3 - 3 matrix satisying M - 0- 1- 0 - - - -1- 2- 3 - M- 1- -1- 0 - 1- 1- -1 - and M - 1- 1- 1 - - - 0- 0- 12 -Then- the sum of the diagonal entries of M is

Let M = [ a_1 amp; a_2 amp;a_3; b_1 amp; b_2 amp; b_3; c_1 amp; c_2 amp; c_3 ] ∴ M [ 0; 1; 0 ] = [ 1; 2; 3 ] M [ 1; 1; 0 ]=[ 1; 1; 1 ] ...

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Equality of Matrices

Let M be a 3 ...

Question

Let M be a $3 \times 3$ matrix satisying $M ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦, M ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 - 1 \end{matrix} ⎤ ⎥ ⎦, a n d M ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0012 \end{matrix} ⎤ ⎥ ⎦ .$
Then, the sum of the diagonal entries of M is ___

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M

3 \times 3

M ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦, M ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 - 1 \end{matrix} ⎤ ⎥ ⎦

M ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0012 \end{matrix} ⎤ ⎥ ⎦

M

3

\times

3

M ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦, M ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 - 1 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0012 \end{matrix} ⎤ ⎥ ⎦

M

3 \times 3

M ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦, M ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 - 1 \end{matrix} ⎤ ⎥ ⎦; M ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0012 \end{matrix} ⎤ ⎥ ⎦

M

3 \times 3

M ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦, M ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 - 1 \end{matrix} ⎤ ⎥ ⎦, a n d M ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0012 \end{matrix} ⎤ ⎥ ⎦ .

M

3 \times 3

{0, 1, 2}

M^{T} M

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