MATHEMATICS FOR MACHINE
LEARNING
Geometric Vectors - correct answerGeometric vectors are directed segments that can
be drawn (at least in two dimensions). Two geometric vectors, →x and →y, can be
added, such that →x+→y=→z is another geometric vector.
One sample use case of geometric vectors is in physics, where they are used to
represent forces, velocities, and other physical quantities.
How many solution does a System of Linear Equations has? - correct answerThe
general form of a system of linear equations has either no, exactly one, or infinitely
many solutions.
Linear Equations - correct answerLinear equations are mathematical equations that
express a linear relationship between two or more variables.
They are often used to model real-world phenomena, such as the relationship between
the price of a product and the quantity demanded, or the relationship between the
speed of an object and the time it takes to travel a certain distance.
Matrices - correct answerMatrices are a powerful tool for representing systems of linear
equations in a compact and efficient manner. They can be used to find solutions to
these systems, and to perform a variety of other operations, such as matrix
multiplication, matrix inversion, and matrix decomposition.
Matrices are also used in a wide variety of applications, including computer graphics,
signal processing, and machine learning.
Polynomials - correct answerPolynomials are also vectors. Two polynomials can be
added together, which results in another polynomial; and they can be multiplied by a
scalar λ∈R, and the result is a polynomial as well.
One sample use case of polynomials is in computer graphics, where they are used to
represent curves and surfaces.
System of Linear Equations - correct answerA system of linear equations is a collection
of one or more linear equations involving the same set of variables that can be
expressed in the form Ax = b, where A is a matrix, x is a column vector of variables, and
b is a column vector of constants.
e.g. in the field of economics, systems of linear equations can be used to model and
solve complex economic systems involving supply and demand, market equilibrium, and
resource allocation
LEARNING
Geometric Vectors - correct answerGeometric vectors are directed segments that can
be drawn (at least in two dimensions). Two geometric vectors, →x and →y, can be
added, such that →x+→y=→z is another geometric vector.
One sample use case of geometric vectors is in physics, where they are used to
represent forces, velocities, and other physical quantities.
How many solution does a System of Linear Equations has? - correct answerThe
general form of a system of linear equations has either no, exactly one, or infinitely
many solutions.
Linear Equations - correct answerLinear equations are mathematical equations that
express a linear relationship between two or more variables.
They are often used to model real-world phenomena, such as the relationship between
the price of a product and the quantity demanded, or the relationship between the
speed of an object and the time it takes to travel a certain distance.
Matrices - correct answerMatrices are a powerful tool for representing systems of linear
equations in a compact and efficient manner. They can be used to find solutions to
these systems, and to perform a variety of other operations, such as matrix
multiplication, matrix inversion, and matrix decomposition.
Matrices are also used in a wide variety of applications, including computer graphics,
signal processing, and machine learning.
Polynomials - correct answerPolynomials are also vectors. Two polynomials can be
added together, which results in another polynomial; and they can be multiplied by a
scalar λ∈R, and the result is a polynomial as well.
One sample use case of polynomials is in computer graphics, where they are used to
represent curves and surfaces.
System of Linear Equations - correct answerA system of linear equations is a collection
of one or more linear equations involving the same set of variables that can be
expressed in the form Ax = b, where A is a matrix, x is a column vector of variables, and
b is a column vector of constants.
e.g. in the field of economics, systems of linear equations can be used to model and
solve complex economic systems involving supply and demand, market equilibrium, and
resource allocation
