Section 9

Systems of equations

fundamentalviz

{a_{1} x + b_{1} y = c_{1} a_{2} x + b_{2} y = c_{2}

Two linear equations in two unknowns.

intermediateviz

A x = b

Represents a linear system in matrix notation.

intermediateviz

[A ∣ b]

Collects coefficients and constant terms.

intermediateviz

R_{i} \leftrightarrow R_{j}; R_{i} \leftarrow c R_{i}; R_{i} \leftarrow R_{i} + c R_{j}

Foundation of Gaussian and Gauss–Jordan elimination.

intermediateviz

rank (A) = rank ([A ∣ b]) = n o rank (A) = rank ([A ∣ b]) < n o rank (A) \neq = rank ([A ∣ b])

Classifies systems according to ranks and the number of unknowns.