Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Show that the function
$F [\begin{matrix} a & b & c \\ d & e & f \\ g & h & j \end{matrix}] = b f g$
is linear in all three columns and in all three rows. See Example 6. Is F alternating on the columns? See Example 4.

Therefore, function F is linear in all rows and columns, but it's not alternating on the columns.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

Given matrix,

$F [\begin{matrix} a & b & c \\ d & e & f \\ g & h & j \end{matrix}] = b f g$

Step 2: To show the function

Given,

$F [\begin{matrix} a & b & c \\ d & e & f \\ g & h & j \end{matrix}] = b f g$

Contains one factor from each row and from each column, therefore, it's linear in all three rows and all three columns.

On the other hand, we can see that, for example,

role="math" localid="1659505275434" $F ([\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}]) = 1$ , but if we switch the second and third column of this matrix, we have

$F ([\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}]) = 1$ , which means that F is not alternating on the columns.

Therefore, function F is linear in all rows and columns, but it's not alternating on the

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Linear Algebra With Applications

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Short Answer

Show that the function
$F [\begin{matrix} a & b & c \\ d & e & f \\ g & h & j \end{matrix}] = b f g$
is linear in all three columns and in all three rows. See Example 6. Is F alternating on the columns? See Example 4.

Step by Step Solution

Step 1: Given

Step 2: To show the function

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Linear Algebra With Applications

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Short Answer

Show that the function F[abcdefghj]=bfgis linear in all three columns and in all three rows. See Example 6. Is F alternating on the columns? See Example 4.

Step by Step Solution

Step 1: Given

Step 2: To show the function

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Show that the function
$F [\begin{matrix} a & b & c \\ d & e & f \\ g & h & j \end{matrix}] = b f g$
is linear in all three columns and in all three rows. See Example 6. Is F alternating on the columns? See Example 4.