SUMMARY
The determinant of the matrix expression 4A-1, given that det(A) = 7, can be calculated using properties of determinants. Specifically, scaling a matrix by a scalar multiplies the determinant by that scalar raised to the power of the matrix size. Therefore, det(4A) = 4^3 * det(A) = 64 * 7 = 448. Since det(A-1) = 1/det(A), we find that det(4A-1) = det(4A) * det(A-1) = 448 * (1/7) = 64.
PREREQUISITES
- Understanding of matrix determinants
- Familiarity with properties of determinants, including scaling and inverses
- Knowledge of 3x3 matrices
- Basic algebraic manipulation skills
NEXT STEPS
- Study the properties of determinants in linear algebra
- Learn about matrix inverses and their determinants
- Explore scalar multiplication effects on determinants
- Practice solving determinant problems with various matrix sizes
USEFUL FOR
Students studying linear algebra, mathematics educators, and anyone looking to deepen their understanding of matrix properties and determinants.