If A is an n n matrix and x is a vector in Rn, then the

Chapter 1, Problem 1

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QUESTION:

If A is an \(n \times n\) matrix and \(\vec{x}\) is a vector in \(\mathbb{R}^{n}\), then the product \(A \vec{x}\) is a linear combination of the columns of matrix A.

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QUESTION:

If A is an \(n \times n\) matrix and \(\vec{x}\) is a vector in \(\mathbb{R}^{n}\), then the product \(A \vec{x}\) is a linear combination of the columns of matrix A.

ANSWER:

Step 1 of 3

Given:

Ais a  \(n \times n\) matrix and \(\vec{x}\) is a vector in \(\mathbb{R}^{n}\)

The objective is to show that the product \(A \vec{x}\) is a linear combination of the columns of matrix A

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