find the matrix of the lineartransformation T : V S W with respect to the bases B and Cof V and W, respectively. Verify Theorem 6.26 for the vector vby computing T(v) directly and using the theorem.

S343 Section 3.2 Notes- Solutions of Linear Homogeneous Equations; The Wronskian 9-27-16 Theorem 3.2.1- Existence and Uniqueness Theorem ′′ ( ) ′ ( ) ( ) ( ) ′( ) ′ o Consider initial value problem + + = , 0 = 0 0 = 0here ,, continuous on open interval containing 0 o This problem has exactly 1 (unique) solution = that exists throughout 2 ′′ ′ Ex. Find the maximal interval of existence of the solution of − 4 + + sin = ln where | | 1 = 2, 1 = 3. ′′ ′ sin ln | o + 2 + 2 = 2 −4 −4 −4 o = → continuous on −∞,−2 ∪ −2,2 ∪ 2,∞ ) ( ) −4 sin o = 2 → continuous on −∞,−2 ∪ −2,2 ∪ 2,∞ ) ( ) −4 o = ln → continuous on 0,2 ∪ 2,∞ ) ( ) o 0= 1, so maximal interval is 0,2( ) Theorem 3.2.2- Principle of Superposition o If