Prove that every matrix in $GL_2(\mathbb{R})$ is a product of at most 4 elementary matrices.
$GL_2(\mathbb{R})$ = set of invertible matrices of order 2×2.
How should i approach to prove this?
2026-03-28 01:07:15.1774660035
Prove that every matrix in $GL_2(\mathbb{R})$ is a product of at most 4 elementary matrices.
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Use the fact that every elementary matrix operation can be achieved by multiplying the matrix with a suitable elementary matrix, as explained here. Now how many elementary matrix operations you need to perform to bring a matrix from $GL_2(\mathbb{R})$ to an elementary matrix?