Download   (Some) Matrices and Determinants 

 (Some) Matrices and Determinants Note: In the matrices below, lower case letters may be either numbers or variable expressions. • For a 2x2 matrix A, the determinate ∆ is calculated by: •
∆
For a 3x3 matrix A, the determinant ∆ is calculated by: |
|
|
∆
The second representation of the determinant matrix is just to show where the math comes from. Procedure: 1. Repeat the first two columns (after red dashed line) 2. Multiply diagonals. From left to right is a positive contribution, from right to left is a negative contribution (note that signs may be changed by actual matrix components when multiplication performed). Cramer’s Rule (aka some Dinosaur Math) Given three matrices A (nxn), X (nx1) and Y (nx1), where n is an integer, ,
You can solve for unknowns X1, X2, …, Xn by solving for a series of determinants and taking appropriate ratios. As above, ∆ = |A| For the remainder of the required determinants, i=1…n, replace the ith column in the original A matrix with the Y matrix as follows: 1
3
2
∆
. . . . . . . ∆
All the way through . . . . ∆
Then: ∆
∆
,
∆
∆
,…
∆
∆
1
1