Problem 1. (10 points) Consider the space X = R22 and the map L XX defined as traceX -traceX L:X X = X 0 0 1. Show that L is a linear map; 2. Find the matrix representation M = mat L in the canonical basis of X X=span { ( ) ( ) ( ) ( )} 3. Find a basis of the range space R{L} CX and a basis of the null space N{L} C X; 4. Is L is epic and/or monic? Explain; 5. Determine the solution X(-): RX of the linear differential equation x(t) = L(x(t)) where X(0) = X0 X 2012 2011 Xo = 2021 2022.