Mathematics for Machine Learning Quiz

What is the derivative of `x^3`?

• 3x

• 3x^2

• x^2

• 3

Answer explanation

The derivative of `x^3` is found using the power rule, which states that the derivative of `x^n` is `n*x^(n-1)`. Here, `n` is 3, so the derivative is `3*x^(3-1)`, which simplifies to `3x^2`. Thus, the correct answer is `3x^2`.

What is the dot product of [1, 2] and [3, 4]?

• 7

• 11

• 10

• 5

Answer explanation

The dot product is calculated as (1*3) + (2*4) = 3 + 8 = 11. Therefore, the correct answer is 11.

What is a matrix?

• A set

• A table of numbers

• A list

• A graph

Answer explanation

A matrix is defined as a table of numbers arranged in rows and columns, making 'A table of numbers' the correct choice. It is not simply a set, list, or graph.

Which matrix is used for linear transformations?

• Identity matrix

• Diagonal matrix

• Square matrix

• All of the above

Answer explanation

All types of matrices, including identity, diagonal, and square matrices, can be used for linear transformations. Each serves specific purposes in transforming vectors in different ways.

What is an eigenvalue?

• A scalar value

• A matrix row

• A vector

• A determinant

Answer explanation

An eigenvalue is defined as a scalar value that indicates how much a corresponding eigenvector is stretched or compressed during a linear transformation. Thus, the correct answer is 'A scalar value'.

What is the rank of a matrix?

• Number of rows

• Number of columns

• Number of linearly independent rows/columns

• Determinant

Answer explanation

The rank of a matrix is defined as the number of linearly independent rows or columns. This indicates the dimension of the vector space spanned by its rows or columns, making it the correct choice.

What is the trace of a matrix?

• Sum of diagonal elements

• Sum of all elements

• Product of diagonal elements

• Determinant

Answer explanation

The trace of a matrix is defined as the sum of its diagonal elements. This means you add together the elements that run from the top left to the bottom right of the matrix, making 'Sum of diagonal elements' the correct choice.

What is gradient descent used for?

• Finding minima

• Finding maxima

• Finding derivatives

• Solving equations

Answer explanation

Gradient descent is an optimization algorithm primarily used for finding minima of functions. It iteratively adjusts parameters to reduce the value of a cost function, making 'Finding minima' the correct choice.

What does singular mean in linear algebra?

• Non-invertible

• Symmetric

• Non-diagonalizable

• Identity

Answer explanation

In linear algebra, a matrix is called singular if it is non-invertible, meaning it does not have an inverse. This occurs when its determinant is zero, indicating that the matrix does not span the entire space.

What is the determinant of a matrix used for?

• Finding eigenvalues

• Checking invertibility

• Finding rank

• Solving systems

Answer explanation

The determinant of a matrix is crucial for checking its invertibility. A matrix is invertible if its determinant is non-zero. Thus, the correct answer is 'Checking invertibility'.