Practice Linear Transformations And Systems Of Linear Equations (28.9) - Linear Transformations

Practice: Linear Transformations and Systems of Linear Equations

Lesson 28.9Linear Transformations

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9 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is a linear transformation?
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Think about how vectors interact under transformations.
Question 2.
What condition must be met for a solution to exist in a linear system?
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Revisit how the image relates to the output of the transformation.
3Question 3.
What does the kernel of a linear transformation represent?
- Set of all output vectors
- Set of vectors mapping to zero
- The transformation function
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Consider what happens to vectors under a transformation.
4Question 4.
True or False: A solution exists for all systems of linear equations.
- True
- False
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Revisit the conditions for the existence of solutions.
Question 5.
Given a system of equations defined by matrix A, determine if the vector b can be expressed as a linear combination of A's columns. What steps would you take?
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Look for free variables indicating multiple solutions or restricted solutions.
Question 6.
Consider a linear transformation that maps R^2 to R^2. How would you determine the kernel and image geometrically?
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Sketch out how vectors transform using the mapping.

5 more questions in this section. Enroll free to practise them all.