Work through a series of matrix calculations covering multiplication, determinants, and eigenvalues.
Formula Sheet
(AB)ᵢⱼ = Σ AᵢₖBₖⱼdet([[a,b],[c,d]]) = ad−bcdet(A−λI)=0 for eigenvaluesMultiply: A = [[1,2],[3,4]], B = [[2,0],[1,3]]. What is entry (1,1) of AB (top-left)?
What is the determinant of A = [[3,1],[2,4]]?
For matrix A = [[2,0],[0,3]], what are the eigenvalues?
A matrix is invertible (non-singular) if and only if its determinant is: