This page explores the matrix equation \(Ax = b\), defining key concepts like consistency conditions, the relationship between matrix and vector forms, and the significance of spans. It explains that ...This page explores the matrix equation \(Ax = b\), defining key concepts like consistency conditions, the relationship between matrix and vector forms, and the significance of spans. It explains that for \(Ax = b\) to have solutions, the vector \(b\) must lie within the span of \(A\)'s columns. Systems have solutions for all \(b\) if \(A\) has a pivot in every row.
