brodidit for students
Home / Practice / NET / Mathematics / Vectors, matrices and complex numbers
Vectors, matrices and complex numbers
8 NET Mathematics questions with answers and explanations.
Printable worksheet with answer key
-
What is the eccentricity of the ellipse x² / 25 + y² / 16 = 1?
- 1 4/5
- 2 9/25
- 3 3/5
- 4 5/4
Show answer
Correct answer: 3/5
Here a² = 25 and b² = 16. e = sqrt(1 - b² / a²) = sqrt(9/25) = 3/5.
-
What is the angle between the vectors (1, 0) and (1, 1)?
- 1 90 degrees
- 2 60 degrees
- 3 45 degrees
- 4 30 degrees
Show answer
Correct answer: 45 degrees
cos(theta) = (1 x 1 + 0 x 1) / (1 x sqrt(2)) = 1 / sqrt(2), so theta = 45 degrees.
-
What is the magnitude of the cross product of a = (2, 0, 0) and b = (0, 3, 0)?
- 1 1
- 2 5
- 3 0
- 4 6
Show answer
Correct answer: 6
The vectors are perpendicular, so |a x b| = |a||b| = 2 x 3 = 6.
-
What are the eigenvalues of the matrix [[2, 0], [0, 3]]?
- 1 2 and -3
- 2 2 and 3
- 3 1 and 6
- 4 0 and 5
Show answer
Correct answer: 2 and 3
The eigenvalues of a diagonal matrix are its diagonal entries.
-
If A is a 2 x 2 matrix with det A = 3, what is det(2A)?
- 1 9
- 2 12
- 3 6
- 4 24
Show answer
Correct answer: 12
For a 2 x 2 matrix, det(kA) = k² det(A) = 4 x 3 = 12.
-
What is (1 + i) / (1 - i)?
- 1 i
- 2 -i
- 3 -1
- 4 1
Show answer
Correct answer: i
Multiply top and bottom by (1 + i): (1 + i)² / 2 = 2i / 2 = i.
-
What is the argument of the complex number -1?
- 1 pi
- 2 -pi / 2
- 3 0
- 4 pi / 2
Show answer
Correct answer: pi
The number -1 lies on the negative real axis, at an angle of pi from the positive real axis.
-
What is the sum of the three cube roots of unity?
- 1 -1
- 2 1
- 3 0
- 4 3
Show answer
Correct answer: 0
The roots of z³ = 1 sum to the negative of the coefficient of z², which is 0.