Master Linear Algebra Quiz

Test your knowledge on the fundamental concepts of Linear Algebra with this challenging quiz! See how well you know matrices, vectors, and linear transformations.

published on July 14
1/12

What is the result of multiplying a 2x3 matrix by a 3x4 matrix?

What is the result of multiplying a 2x3 matrix by a 3x4 matrix?
A 2x4 matrix
A 5x5 matrix
A 3x3 matrix
A 2x7 matrix
2/12

What is the determinant of a 2x2 matrix [a b, c d] equal to?

What is the determinant of a 2x2 matrix [a b, c d] equal to?
ad - bc
ac - bd
a + d
b - c
3/12

Which of the following is NOT a vector operation?

Which of the following is NOT a vector operation?
Scalar multiplication
Addition
Matrix multiplication
Dot product
4/12

What is the rank of a 3x3 identity matrix?

3
1
2
0
5/12

The set of vectors that form a basis for a vector space must be ___________.

The set of vectors that form a basis for a vector space must be ___________.
Linearly independent
Orthogonal
Scalar multiples of each other
Null vectors
6/12

Which of the following is a property of an invertible matrix?

Which of the following is a property of an invertible matrix?
Its determinant is non-zero
It has a rank of 0
Its columns are linearly dependent
It has a null space
7/12

What is the dot product of two perpendicular vectors?

0
1
-1
2
8/12

The solution to a system of linear equations can be represented as ____________.

An intersection point
An infinite set of points
A vector
A line
9/12

What is the characteristic polynomial of a 2x2 matrix?

What is the characteristic polynomial of a 2x2 matrix?
λ^2 - (a + d)λ + (ad - bc)
λ - det(A)
λ^3 - aλ^2 + bλ - c
(a + d)λ - 1
10/12

Which matrix operation is equivalent to swapping rows?

Which matrix operation is equivalent to swapping rows?
Elementary row operation
Transposition
Matrix inversion
Eigendecomposition
11/12

What does it mean for a matrix to be symmetric?

Its transpose equals itself
Its determinant is negative
It has complex eigenvalues
It is singular
12/12

In a 4x4 matrix, how many minors of order 2 can be calculated?

16
4
8
12