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Q3E

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Linear Algebra With Applications

Found in: Page 1

Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Find the rank of the matrices in 2 through 4.
3. $[\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}]$

The rank of the matrix $[\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}]$ is, $1$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Find row reduce echelon form

The number of leading 1’s in $rref (A)$ represents the rank of a matrix A denoted by $rank (A)$ .

The given matrix is, $[\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}]$ .

The reduced row echelon form of the given matrix is:

$r r e f [\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}] = [\begin{matrix} 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix}]$

Step 2: Determine the rank of a matrix.

The number of leading 1’s in the matrix $[\begin{matrix} 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix}]$ are $1$ .

Hence, the rank of the given matrix is 1.

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