← MATH 01210 · Linear Algebra
MATH 01210 · Systems & matrices
Determinants
Definition
det A is a scalar measuring oriented volume scaling of the linear map A. det=0 ⇔ singular. Multiplicative: det(AB)=det A det B.
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Compute via cofactor expansion or row-reduction (track swap/scale factors).
Row swap flips sign; scaling a row scales det; adding multiple of a row to another does not change det.
Geometric: |det| = area/volume of parallelepiped spanned by columns.
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Attempt each problem first, then open the worked solution.
1.Compute det of [[2,1],[5,3]] two ways.