5.2a plot linear transformations

In summary, the task is to find three matrices for different transformations: rotation by $\dfrac{\pi}{4}$, shear along $x$ by a factor of $k$, and reflection by the line $\theta$. The matrices, their determinants, and eigenvalues need to be reported. The question also mentions using only matrices from the website for all three transformations.
  • #1

karush

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ok we are supposed to go to here

Find 3 different matrices that reflect the following transformations, report the matrix, the determinant, and the eigenvalues.

1. Rotation by $\dfrac{\pi}{4}$
2. Shear along $x$ by a factor of $k$
3. Reflection by the line $\theta$

there are some more but the site asked for doesn't return the transformed matrix just a morphed image
also I presume we doing all 3 matrices with just the matrix's used in the site

I tried geogebra and W|A also but the plots didn't look like vectors

anyway this is due on Friday so hope I can get it right. I am sure the answer is relatively simple
,
 
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  • #2
ok here is what I did for shear k=2
probab'y would have been better for $k=\sqrt{2}$

Screenshot 2021-03-17 10.45.42 AM.png
 
  • #3
karush said:
also I presume we doing all 3 matrices with just the matrix's used in the site
I don't understand this phrase. What matrix is used on the site? To me the problem seems to ask to find three separate matrices, their determinants and their eigenvalues.
 

1. What is a linear transformation?

A linear transformation is a function that maps a set of points in one coordinate system to a set of points in another coordinate system in a way that preserves straight lines. In other words, it is a transformation that maintains the linearity of the original data.

2. What does the "5.2a" in "5.2a plot linear transformations" refer to?

The "5.2a" refers to the specific section or topic within a larger curriculum or textbook that covers the concept of plotting linear transformations. It is a way to organize and categorize different concepts within a larger subject area.

3. How do you plot linear transformations?

To plot linear transformations, you first need to identify the original points or data that you want to transform. Then, using a graph or coordinate system, you can apply the transformation to each point by following the specific rules or equations for that transformation. Finally, you plot the new points on the graph to visualize the transformation.

4. What are some common examples of linear transformations?

Some common examples of linear transformations include translation, scaling, rotation, and shearing. Translation involves moving all points in a certain direction by a certain distance. Scaling involves stretching or shrinking the points by a certain factor. Rotation involves rotating the points around a fixed point. Shearing involves changing the shape of the points by stretching one axis while compressing the other.

5. Why are linear transformations important in science?

Linear transformations are important in science because they allow us to analyze and understand complex data by simplifying it into a more manageable form. They also help us to identify patterns and relationships between different variables. Additionally, linear transformations are used in many scientific fields such as physics, engineering, and statistics to model and predict real-world phenomena.

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