TBIL-LA Geometric Properties of Linear Maps (GT)

Chapter 5 Geometric Properties of Linear Maps (GT)

How do we understand linear maps geometrically?

By the end of this chapter, you should be able to...

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Describe how a row operation affects the determinant of a matrix.
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Compute the determinant of a $4 \times 4$ matrix.
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Find the eigenvalues of a $2 \times 2$ matrix.
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Find a basis for the eigenspace of a $4 \times 4$ matrix associated with a given eigenvalue.

Before beginning this chapter, you should be able to...

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Calculate the area of a parallelogram.
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  Review: Khan Academy ¹
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Recall and use the definition of a linear transformation.
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  Review: Section 3.1
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Find the matrix corresponding to a linear transformation of Euclidean spaces.
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  Review: Section 3.2
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Find all roots of quadratic polynomials (including complex ones).
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  Review: Khan Academy ², YouTube (1)³, YouTube (2)⁴
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Interpret the statement “ $A$ is an invertible matrix” in many equivalent ways in different contexts.
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  Review: Section 4.3

www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-geometry-topic/cc-6th-parallelogram-area/v/intuition-for-area-of-a-parallelogram

www.khanacademy.org/math/algebra-home/alg-polynomials/alg-factoring-polynomials-quadratic-forms/v/factoring-trinomials-by-grouping-5

youtu.be/Aa-v1EK7DR4

www.youtube.com/watch?v=2yBhDsNE0w