Calculating the Determinant
Determinants of Special Matrices
Determinants of Manipulated Matrices
Invertibility
Cramer's Rule How to Examples Exercise
How to:
In this section, we will work with NxN matrices, Aand B, and their determinants, det(A) and det(B).
So, having calculated A and B's determinants, we can quickly and easily find the determinants of several other matrices without even using MATLAB:
1) A' (the transpose of A) -- det(A') = det(A)
2) inv(A) (the inverse of A) -- det(inv(A)) = 1 / det(A)
3) A*B (the product of A and B) -- det(A*B) = det(A)*det(B)
Examples:
Let's work with the same matrix as last section, A = 1 2 5 -1; 7 -3 7 4; 1 1 0 10; -1 -9 -9 0], whose determinant we've already calculated to be det(A) = 1010.
Now, without even calculating A's transpose, inverse, or the product of A with itself, we know their determinants:
det(A') = det(A) = 1010
det(inv(A)) = 1 / det(A) = 1/1010 = .0009901
det(A*A) = det(A)*det(A) = 1010*1010 = 1020100
Exercise: