Provide solution to the following questions:
1. Evaluate the following: ∫x sin?3x dx
2. If A =
then for what value of α is A an identity matrix?
3. The line y = mx + 1 is a tangent to the curve y2 = 4x. Find the value of m.
4. Solve the following differential equation: (x2 - y2) dx + 2xy dy = 0.
5. Solve system of linear equations, using matrix method.
x - y + 2z = 7
3x + 4y - 5z = -5
2x - y + 3z = 12