3. Let A - 3202 3219 3 3 0 5 0 -2 -3 0 2 10 3 2 Evaluate det(A) by a cofactor expansion along a row or column of your choice. Is A invertible?

Problem #1: Let V be the set of all ordered pairs of real numbers (µ₁, 42) with u₂ > 0. Consider the following addition and scalar multiplication operations on u = = (u₁, u₂) and v = (V₁, V2): u + v = (u₁ + v₁ + 4,7u2v2), ku = (ku1, ku2) Use the above operations for the following parts. (a) Compute u + v for u = (-2,3) and v = = (-2,2). (b) If the set V satisfies Axiom 4 of a vector space (the existence of a zero vector), what would be the zero vector? (c) If u = (5,5), what would be the negative of the vector u referred to in Axiom 5 of a vector space? (Don't forget to use your answer to part (b) here!)

Example:3 Verify Cayley-Hamilton theorem, and find A-1 [2 A=0 1 [1 1 2.

3) Determine the inverse lapley transform of 105² +42s + 24 F(s) 53 + 45² +35