MCQ Subject: Engineering Mathematics

A 3×3 diagonal matrix has diagonal entries 2, 2, and 5. How many distinct eigenvalues does this matrix have?

A 3×3 matrix A has an inverse if which of the following is true?

In the context of systems of linear differential equations, what is the primary use of eigenvalues of the coefficient matrix?

Which characteristic uniquely defines an orthogonal matrix?

A 2×2 matrix has a trace of 7 and a determinant of 12. How many distinct eigenvalues does it have?

In a class, 60% of students like Math, 50% like Physics, and 30% like both. What is the probability a student likes Physics given they like Math?

Which of the following properties of the Laplace Transform is correctly applied to solve a differential equation with initial conditions?

Which of the following is equal to the trace of a square matrix?

For a 2×2 matrix A with eigenvalues λ₁ and λ₂, which statement is correct?

What is the Laplace Transform of the function f(t) = t^2 * sin(3t)?