3.2 Determinants; Mtx Inverses. Theorem 1- Product Theorem. If A and B are (n x n), then det(AB)=det A det B (come back to prove later) Show true for 2 x 2 of random variables. Extension. Using induction, we could show that: det(A 1 A 2 …A k ) = detA 1 detA 2 …detA k
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3.2 Determinants; Mtx Inverses
c ≠ 0
If A is an invertible (n x n) matrix, the solution to the system AX = B of n equations in n variables is:
Where Ai is the matrix obtained by replacing column i of A with the column matrix B.
This is not very practical for large matrices, and it does not give a solution when A is not invertible