▸Determinant = 8: this matrix is invertible.
- The determinant is 8, which is non-zero, so the matrix is invertible (non-singular).
- The trace is 7, the sum of the main diagonal entries. It also equals the sum of all eigenvalues.
- The rank is 3 (full rank for a 3x3 matrix), confirming all rows are linearly independent.
- A positive determinant means the linear transformation preserves orientation. Its absolute value gives the scale factor by which the transformation stretches area (in 2D) or volume (in 3D).
Next stepThe absolute value of the determinant, 8, is the scale factor of the linear transformation defined by this matrix.