Notice: This page requires JavaScript to function properly.
Please enable JavaScript in your browser settings or update your browser.Challenge: Figures' Linear Transformations | Linear Algebra
Mathematics for Data Analysis and Modeling
course content

Course Content

Mathematics for Data Analysis and Modeling

Mathematics for Data Analysis and Modeling

1. Basic Mathematical Concepts and Definitions
What is a Function?What are Number Series?Sum of Elements of The SeriesChallenge: Calculating Sum of Geometric ProgressionVectors and Matrices
2. Linear Algebra
Numerical Operations on Vectors and MatricesChallenge: Calculate the Matrix Multiplication ResultMatrix DeterminantScaling Factor of the Linear TransformationChallenge: Figures' Linear TransformationsInversed and Transposed MatricesSystem of Linear EquationsChallenge: Solving the Task Using SLEEigenvalues and Eigenvectors
3. Mathematical Analysis
Derivative of the FunctionPartial Derivative of the FunctionChallenge: Solving Task Using DerivativeOptimization ProblemChallenge: Solving the Optimisation ProblemGradient Descent MethodChallenge: Optimising Function Of Multiple Variables

Challenge: Figures' Linear Transformations

Task

Linear transformations of the figures are commonly used in computer graphics. There are 2 main types of linear transformations:

  1. Rotation transformation rotates a figure around a specific point or axis.
  2. Scale transformation resizes a figure by changing its size along each axis.

Your task is to apply all these transformations to a rectangle one by one. As a result, we will have a composition of transformations:

  1. Сreate rotation matrix that rotates a figure by np.pi / 3 degrees.
  2. Create a scaling matrix with the parameters scale_x = 2 and scale_y = 0.5.
  3. Apply the rotation_matrix to the square.
  4. Apply the scaling_matrix to the result of the previous transformation.

Task

Linear transformations of the figures are commonly used in computer graphics. There are 2 main types of linear transformations:

  1. Rotation transformation rotates a figure around a specific point or axis.
  2. Scale transformation resizes a figure by changing its size along each axis.

Your task is to apply all these transformations to a rectangle one by one. As a result, we will have a composition of transformations:

  1. Сreate rotation matrix that rotates a figure by np.pi / 3 degrees.
  2. Create a scaling matrix with the parameters scale_x = 2 and scale_y = 0.5.
  3. Apply the rotation_matrix to the square.
  4. Apply the scaling_matrix to the result of the previous transformation.

Everything was clear?

Section 2. Chapter 5
toggle bottom row

Challenge: Figures' Linear Transformations

Task

Linear transformations of the figures are commonly used in computer graphics. There are 2 main types of linear transformations:

  1. Rotation transformation rotates a figure around a specific point or axis.
  2. Scale transformation resizes a figure by changing its size along each axis.

Your task is to apply all these transformations to a rectangle one by one. As a result, we will have a composition of transformations:

  1. Сreate rotation matrix that rotates a figure by np.pi / 3 degrees.
  2. Create a scaling matrix with the parameters scale_x = 2 and scale_y = 0.5.
  3. Apply the rotation_matrix to the square.
  4. Apply the scaling_matrix to the result of the previous transformation.

Task

Linear transformations of the figures are commonly used in computer graphics. There are 2 main types of linear transformations:

  1. Rotation transformation rotates a figure around a specific point or axis.
  2. Scale transformation resizes a figure by changing its size along each axis.

Your task is to apply all these transformations to a rectangle one by one. As a result, we will have a composition of transformations:

  1. Сreate rotation matrix that rotates a figure by np.pi / 3 degrees.
  2. Create a scaling matrix with the parameters scale_x = 2 and scale_y = 0.5.
  3. Apply the rotation_matrix to the square.
  4. Apply the scaling_matrix to the result of the previous transformation.

Everything was clear?

Section 2. Chapter 5
toggle bottom row

Challenge: Figures' Linear Transformations

Task

Linear transformations of the figures are commonly used in computer graphics. There are 2 main types of linear transformations:

  1. Rotation transformation rotates a figure around a specific point or axis.
  2. Scale transformation resizes a figure by changing its size along each axis.

Your task is to apply all these transformations to a rectangle one by one. As a result, we will have a composition of transformations:

  1. Сreate rotation matrix that rotates a figure by np.pi / 3 degrees.
  2. Create a scaling matrix with the parameters scale_x = 2 and scale_y = 0.5.
  3. Apply the rotation_matrix to the square.
  4. Apply the scaling_matrix to the result of the previous transformation.

Task

Linear transformations of the figures are commonly used in computer graphics. There are 2 main types of linear transformations:

  1. Rotation transformation rotates a figure around a specific point or axis.
  2. Scale transformation resizes a figure by changing its size along each axis.

Your task is to apply all these transformations to a rectangle one by one. As a result, we will have a composition of transformations:

  1. Сreate rotation matrix that rotates a figure by np.pi / 3 degrees.
  2. Create a scaling matrix with the parameters scale_x = 2 and scale_y = 0.5.
  3. Apply the rotation_matrix to the square.
  4. Apply the scaling_matrix to the result of the previous transformation.

Everything was clear?

Task

Linear transformations of the figures are commonly used in computer graphics. There are 2 main types of linear transformations:

  1. Rotation transformation rotates a figure around a specific point or axis.
  2. Scale transformation resizes a figure by changing its size along each axis.

Your task is to apply all these transformations to a rectangle one by one. As a result, we will have a composition of transformations:

  1. Сreate rotation matrix that rotates a figure by np.pi / 3 degrees.
  2. Create a scaling matrix with the parameters scale_x = 2 and scale_y = 0.5.
  3. Apply the rotation_matrix to the square.
  4. Apply the scaling_matrix to the result of the previous transformation.

Section 2. Chapter 5
Switch to desktop for real-world practiceContinue from where you are using one of the options below
We're sorry to hear that something went wrong. What happened?
some-alt