Linear Algebra · Lesson 5
Determinants
The determinant is a single number that captures the "scale factor" of a matrix transformation. It tells you whether a matrix is invertible, how much it stretches or shrinks space, and whether it flips orientation.
Quick Check
1. det([[3, 1], [2, 4]]) = ?
10
14
2
−2
2. A matrix with det = 0 is:
Symmetric
Singular (not invertible)
The identity matrix
Orthogonal
3. If det(A) = 5 and det(B) = 3, then det(AB) = ?
8
15
2
√15
4. A negative determinant means the transformation:
Shrinks space
Flips orientation
Is not defined
Leaves space unchanged