3.4 Determinants
Readings
At this time please read Chapter 3 Section 4 in Understanding Linear Algebra by David Austin.
The determinant of an nxn matrix can be thought of as measuring the area (in the 2x2 case) or volume (in the 3x3 case) of the parallelogram (in the 2x2 case) or box/parallelepiped (in the 3x3 case) formed by the column vectors, together with a sign measuring the orientation of these vectors. We can also think of it as the factor by which area / volume is multiplied when we apply a linear transformation.
Key Takeaways
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- det(AB) = det(A)det(B)
- If A is an nxn matrix, then [latex]det(kA) =k^n det(A)[/latex]
- A is invertible if and only if [latex]det(A) \neq 0[/latex],
Computing determinants examples:
Row reduction operations and their effect on the determinant:
