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Chapter 5 Geometric Properties of Linear Maps (GT)
Learning Outcomes
How do we understand linear maps geometrically?
By the end of this chapter, you should be able to...
Describe how a row operation affects the determinant of a matrix.
Compute the determinant of a \(4\times 4\) matrix.
Find the eigenvalues of a \(2\times 2\) matrix.
Find a basis for the eigenspace of a \(4\times 4\) matrix associated with a given eigenvalue.
Readiness Assurance.
Before beginning this chapter, you should be able to...
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Calculate the area of a parallelogram.
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Recall and use the definition of a linear transformation.
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Find the matrix corresponding to a linear transformation of Euclidean spaces.
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Find all roots of quadratic polynomials (including complex ones).
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Interpret the statement “\(A\) is an invertible matrix” in many equivalent ways in different contexts.
