matrices

• matrices that are the same size

  additively comformable
• matrix form

  n(rows) x m (columns)
• in matrices the order matters
• $(n$ x $m)$$(m$ x $k)$ =


  $(n$ x $k)$ ---> ( m has to be equal)
• matrix multiplication


  row x column
• Determinant of 2x2 matrix

  ad-bc
• determinant of 3x3 matrix

  a(ei-fh)-b(di-gf)+c(dh-eg)
• inverse 2x2 matrix

  1/DetM $[d$ $-b$]

  $[-c$ $a]$
• (AB)$^-$$^1$=


  B$^-$$^1$A$^-$$^1$
• Inverting a 3x3 matrix formula


  1/DetA C$^T$
• Inverse of 3x3 Matrix

  1. Find the determinant
  2. find matrix of minors (massive one then simplify by 2x2)
  3. alternate signs
  4. swap them along diagonal (transpose)
  5. put into formula
• matrices for simultaneous


  1. write the as a matrix
  2. find inverse of number matrix
  3. multiply by the answer matrix to then find x y and z
• Non-singular matrix

  1 unique solution- consistent- meet at a point