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Linear System of Equations

A system of equations consists of unknown variables and  list of equations relating them. 

A Linear System of Equations fulfill the following:

  1. The list of variable (xyz) is scaled by some constant number
  2. The only thing happening to each variable is that they are added to each other
    • no exponents, no multiplication, no sin/cos/tan or other special functions 

A Linear System of Equations is organized by putting scaled variables on the left and constants on the right. Also add Zeros to variables if not present. 

A Linear System of Equations can be transferred to a vector equation with following equation, where A is the matrix holding all the constant coefficients. 

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ide

LSOE_A-transform.gif

LSOE_xvector-landing-on-yvector.gif

Inverse Transformation

Prereq: Determinant 

LSOE_90degree-inverse.gif

identity matrix: 

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When determinant is 0, we can use Rank to describe the number of dimensions in the output of the transformation  

Column Space

Null Space (Kernel) 

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