Exercise 4: Determinant properties
Given the two matrices with det(A)=3 and det(B)=-2
evaluate the following determinants:
- \(\det\left(AB\right)\)
- \(\det\left(BA\right)\)
- \(\det\left(3AB\right)\)
- \(\det\left(A^TB\right)\)
- \(\det\left(A^{-1}B\right)\)
Solution:
- 3x2 =-6
- -2x3 = -6
- 3^3*3*-2=-162
- 3*-2 = -6
- -2/3
Exercise 5: System of equations
Solve the following system of equations: