Provide solution to the following questions:
1. Evaluate the following:
2. If , 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 + 2 xy dy = 0.
5. Solve system of linear equations, using matrix method.
x − y +2z =7
3x +4y −5z =−5
2x − y + 3z = 12