MadScone

113 reputation

	113 reputation	bio	website		visits	member for	1 year, 8 months
13 badges		location			seen	Mar 22 at 10:58

8 Actions

Mar 21	awarded	Notable Question
Nov 20	awarded	Popular Question
Dec 9	awarded	Scholar
Dec 9	accepted	Are three matrices linearly independent and form a basis of $M_2(\mathbb R)$?
Dec 9	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 9	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?
Dec 9	awarded	Student
Dec 9	asked	Are three matrices linearly independent and form a basis of $M_2(\mathbb R)$?