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accepted Are three matrices linearly independent and form a basis of $M_2(\mathbb R)$?
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comment Are three matrices linearly independent and form a basis of $M_2(\mathbb R)$?
Ok thanks, that's all I really needed to know I suppose. I solved the question like this: $$ \operatorname{rref}\left[\begin{array}{ccc|c} -1&1&-1&0 \\ 1&1&1&0 \\ -1&-1&1&0 \\ 1&-1&-1&0 \end{array}\right] = \left[\begin{array}{ccc|c} 1&0&0&0 \\ 0&1&0&0 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right] $$ so the matrices are linearly independent. Assuming that's right, my question has been answered.
Dec
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comment Are three matrices linearly independent and form a basis of $M_2(\mathbb R)$?
So I can rewrite the matrices like this: $$ A = (-1, 1, -1, 1) $$ and so on for the others. How does that simplify the problem? I will get: $$ c_1(-1, 1, -1, 1) + c_2(1, 1, -1, -1) + c_3(-1, 1, 1, -1) = 0 $$ Will that give me four equations?
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asked Are three matrices linearly independent and form a basis of $M_2(\mathbb R)$?