Matrices

Matrices

1. Simple

   • + & -
   • x
   • null- AO=O
   • unit- IA=A
   • inverse
     • 1/ps-qr(mat)
     • Find det, matrix minors, cofactors, transpose, divide

2. Equations

   • A(x y)= (p q) (x y)=A-1(p q)
   • det=0
     • solution
   • det =/ 0
     • no solution
     • infinitely many solutions

3. Transformations

   • Relection
     • x- axis
     • y-axis
     • y=x
     • y=-x
     • y=mx
   • Enlargement (O)
     • scale factor k
   • Stretch
     • x- axis
     • y-axis
   • Shears
     • x -axis
     • y- axis
     • y= x
   • Rotation
     • 90 Clo
     • 180
     • 90 anti
     • +a
   • AreaI = IdetMI xAreaO
   • image line

4. Eigenvectors & Eigenvalues

   • IA-yiI= 0
   • Mt = M-1
   • Diagonalising a 3x3 matrx
     • find matrix P whose columns are the normalised orthogonal eigenvectors of A
     • form the matrix PtAP- this gives a diagonal matric D whose entries in teh leadin diagonal are the eigenvalues of A