MAT 1302 Lecture 6: Homogeneous systems and the null space
25 Jan 2019
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Mat1302 - lecture 6 - homogeneous systems and the null space. Homogeneous system of linear equations: a system of linear equations is homogeneous if the vector of a constant is 0. The solution is obtained by setting all the variables to 0. Trivial solution: the solution set of a homogeneous system. (0,0,0 ) Step 1: turn into augmented matrix and find the reduced row echelon form. Important: a homogeneous system will have many solutions if it has more variables than equations, but it can still have many even if the variables and equations are equal or if there is more equations. The null space of a matrix: when you have the 0 vector equation is written as ax = 0. The null space of a as an m x n matrix is : The null space as linear span: for any m x n matrix, the linear span is written as:
