Lecture 5 (Feb 23)

Homogeneous Linear System Ax=0
(1) Trivial solution
(2) Non-trivial solution if the corresponding reduced echelon form has a free variable.

Ax=b has a solution (called it p) if b in span(a1,...,a_n).

• If trivial solution is the only solution to Ax=0, then p is the unique solution to Ax=b
• If Ax=0 has a non-trivial solution xh, then p+xn is also a solution to Ax=b. This implies Ax=b has infinite many solutions.

Matrix operations.

Matrix-matrix multiplications.