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What are linear combinations, span, and basis, and why do they matter in linear algebra? In this video, we break down how vectors combine to form entire spaces. You'll see how linear combinations work, what it means for vectors to span a space, and how to recognise when a set forms a basis. We also look at linear dependence to understand which vectors genuinely add something new. If you enjoyed this video, check out the full playlist on linear algebra basics: https://www.youtube.com/playlist?list=PLlenrM60CLlM1C6JDdtVBz1LOzIwTSNCm 📌 Timestamps: 0:00 Introduction 0:54 Notation 1:24 Linear Combinations 2:12 Linear Dependence 2:43 Span (What Space Do These Vectors Generate?) 4:45 Formal Definition & Examples 8:34 Basis (Minimal Spanning Sets) 11:12 Dimension
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