Consider the vectors 5, C, and w sketched in the accompanying figure. Find the coordinate vector of w with1 respect to the basis w, C.

M303 Section 2.3 Notes- Characterizations of Invertible Matrices 10-14-16 Theorem 8- Invertible Matrix Theorem (IMT)- Let be × matrix; the following are equivalent: o is invertible o = o has pivot positions in its EF o = has only trivial solution o Columns of are linearly independent o LM :ℝ → ℝ given by = is 1-1 o = has a solution for all o Columns of span ℝ o LM :ℝ → ℝ given by = is onto o There exists an × matrix such that = o There exists an × matrix such that