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Q51E

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Linear Algebra With Applications

Found in: Page 37

Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Consider an n × m matrix A, an r × s matrix B, and a vector _$\vec{x}$in $ℝ^{p}$ . For which values of n, m, r ,s, and p is the product $A (B \vec{x})$ defined?

The values of n, m, r, s and p is the product of $A (B \vec{x})$ is defined are s = p and m = r

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Find the solutions of the systems

For m=r to be defined the number of columns of B must be equal the number of components of $\vec{x}$ .

So columns of B are [s] components of $\vec{x}$ is p

For $A (B \vec{x})$ to be defined we must have m=r

Step 2: Final answer:

The values of n, m, r, s and p is the product of $A (B \vec{x})$ is defined are s = p and m = r

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