Summary of Section: Linear Equations and matrices
Consistent- has a solution
Inconsistent- Does not have a solution
Augmented matrix-
(elementary row operations)
Equivalent- Same solution set
Gauss-Jordan elimination
Reduce from augmented matrix to reduced row-echelon form
(has zeros above and below leading one)
Gaussian elimination
Reduce from augmented matrix to row-echelon form
(Pivot is first-nonzero in row, usually one, zeros above and below)
Generalised row-echelon form
(0 row at bottom and each nonzero row begins with more zeros than previous one)
Homogeneous system
Always has a solution- trivial solution(one solution)/ nontrivial solution(infinite solutions)
Matrix
Rules of matrices
AB not BA A=E1^-1E2^-2E3^-3
AB=AC; does not mean B=C Ax=b (matrix A is invertible)
AB=0; does not mean A=0 or B=0 -matrix equation
x=A^-1b
