Let \(M\) be a 5 by 5 matrix with real coefficients such that \(M^2=2M-I\). Show that the subspace of \(\mathbb {R}^5\) consisting of vectors fixed by \(M\) has dimension at least 3.
Question
Math 6310 • Algebra
Spring 2010 • Question 6
Question
Spring 2010 • Question 6
Let \(M\) be a 5 by 5 matrix with real coefficients such that \(M^2=2M-I\). Show that the subspace of \(\mathbb {R}^5\) consisting of vectors fixed by \(M\) has dimension at least 3.