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Suppose the columns of a matrix $A=\left[\begin{array}{lll}{a_{1}} & {\cdots} & {a_{p}}\end{array}\right]$ are linearly independent. Explain why $\left\{\mathbf{a}_{1}, \ldots, \mathbf{a}_{p}\right\}$ is a basis forCol $A .$

By definition, Col $A$ is a set of all vectors that are linear combinations of columns of $A$ . It is same as if we said that columns of $A$ span $\operatorname{Col} A$ .If they are also linearly independent, $\left\{a_{1}, \ldots, a_{p}\right\}$ is basis for $\operatorname{Col} A$ - simply because definition of basis.

Algebra

Chapter 2

Matrix Algebra

Section 8

Subspaces of Rn

Introduction to Matrices

Campbell University

McMaster University

Baylor University

University of Michigan - Ann Arbor

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nine. This question we have that we given that they warn AP our Linda Lee Independence. So we've given that. So we have these also recall. That's cool moms off A It is these columns off, eh? Ponds? The column space off a ready off. That's so therefore by definition of a busies probate busies. Because we have that's it is literally, literally independence. And we have that. It's also spawns the column space off a. So this would imply that Hey, Juan damping he's a busies four column space off.

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