Image and range of linear transformations
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Intros
Lessons
- Image and Range of Linear Transformations Overview:
- Matrix Transformations
• Transforming from to
• How transforming vector look like visually - The Image of
• : the image of under the transformation
• Finding the image when given
• Finding when given the image - The Range of
• The set of all images
• What the range looks like visually
• How to know if a vector is in the range of
Examples
Lessons
- Consider the matrix
, and let's define → by . Find the images under of
and
- Finding when given the image under
Let's define → by . Let
Find the vector whose image under is , and find out whether is unique. - A vector in the Range of
Let's define → by . Let
Determine if is in the range of the transformation . - Geometric Interpretation of
Use a graph to plot the vectorand its image under the transformation T. You are given that:
Explain what the transformation did to the vector.