# Solving Identity Matrix, Gradient of Tangent and Differential Equations (Math Problem Sample)

solved mathematics problems

Provide solution to the following questions:

⦁ Evaluate the following:

⦁ If , then for what value of α is A an identity matrix?

⦁ The line y = mx + 1 is a tangent to the curve y2 = 4x .Find the value of m.

Gradient of tangent to the curve is the differential of y2 = 4x hence gradient = 4

Thus m = 4

⦁ Solve the following differential equation: (x2 − y2) dx + 2 xy dy = 0.

Provide solution to the following questions:

1 Evaluate the following:

2 If, then for what value of α is A an identity matrix?

Solution for identity matrix of A = matrix A

A-1 =

3 The line y = mx + 1 is a tangent to the curve y2 = 4x .Find the value of m.

Gradient of tangent to the curve is the differential of y2 = 4x hence gradient = 4

Thus m = 4

4 Solve the following differential equation: (x2 − y2) dx + 2 xy dy = 0.

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