SCE Engineering Mathematics 2

Question 1

What is the rank of a 3×3 matrix with two identical rows?

Accepted Answer

At most 2

Answer

Always 3

Answer

Always 1

Answer

Cannot be determined

Question 2

Simpson's 1/3 rule requires how many equally spaced points minimum?

Accepted Answer

3 points (2 intervals)

Answer

2 points (1 interval)

Answer

4 points (3 intervals)

Answer

5 points (4 intervals)

Question 3

What is the gradient of the scalar field φ = x²y + yz²?

Accepted Answer

(2xy, x² + z², 2yz)

Answer

(x²y, yz², 0)

Answer

(2x, 1, 2z)

Answer

(2xy, x², 2yz)

Question 4

A system of linear equations Ax = b has no solution when:

Accepted Answer

rank(A) < rank([A|b])

Answer

rank(A) = rank([A|b])

Answer

det(A) ≠ 0

Answer

A is square

Question 5

The second derivative test classifies a critical point as a saddle point when:

Accepted Answer

D = f_xx·f_yy - (f_xy)² < 0

Answer

D > 0 and f_xx > 0

Answer

D > 0 and f_xx < 0

Answer

D = 0

Question 6

What is the order of the Runge-Kutta method commonly known as RK4?

Accepted Answer

Fourth order

Answer

Second order

Answer

Third order

Answer

First order