Mastering Linear Algebra Quiz

Test your knowledge of linear algebra with these comprehensive questions covering various concepts and calculations.

published on June 12
1/11

What is the equation of a line in slope-intercept form?

What is the equation of a line in slope-intercept form?
y = mx + b
y = ax + b
y = mx - b
y = ax - b
2/11

What is the determinant of a 2x2 matrix?

ad - bc
ab - cd
ac - bd
ad + bc
3/11

What is the dot product of vectors A = [1, 2] and B = [3, 4]?

10
14
11
12
4/11

What is a matrix transpose operation?

What is a matrix transpose operation?
Flipping the matrix diagonally
Interchanging rows and columns
Multiplying all elements by a constant
Inverting the matrix
5/11

How many solutions does a system of linear equations have if it is inconsistent?

How many solutions does a system of linear equations have if it is inconsistent?
Infinite solutions
No solutions
One unique solution
Two unique solutions
6/11

What is the rank of a matrix?

What is the rank of a matrix?
The maximum number of linearly independent rows or columns
The total number of elements in the matrix
The determinant of the matrix
The smallest element in the matrix
7/11

What does it mean for a matrix to be singular?

What does it mean for a matrix to be singular?
It has no determinant
It has an inverse
All elements are equal
It is not invertible
8/11

What is the result of multiplying a matrix by its inverse?

What is the result of multiplying a matrix by its inverse?
The identity matrix
Zero matrix
The original matrix
A matrix with random values
9/11

What is the eigenvector of a matrix used for?

What is the eigenvector of a matrix used for?
Finding the directions that are only scaled by the matrix
Inverting the matrix
Adding new rows or columns to the matrix
Transposing the matrix
10/11

What is a basis of a vector space?

A set of vectors that spans the entire space and is linearly independent
A vector with the most components
A vector with the least components
A vector with all elements equal to zero
11/11

What does it mean for a matrix to be orthogonal?

It has no inverse
Its columns are pairwise orthogonal unit vectors
All elements are equal
It is a square matrix