Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Which of the following functions F of $A = [\begin{matrix} a & b \\ c & d \end{matrix}]$ are linear in both columns? Which are linear in both rows? Which are alternating on the columns? role="math" localid="1659502796300" $a . F (A) = b c b . F (A) = c d c . F (A) = a c d . F (A) = b c - a d e . F (A) = c$

a) Function is linear in both columns and both rows, but it's not alternating on the columns.

b) Function is linear in both columns, but not in both rows, nor is it alternating on the columns.

c) Function is linear in both rows, but not in both columns, nor is it alternating on the columns.

d) Function is linear in both rows and both columns, as well as alternating on the columns.

e) Function is not linear in both rows nor both columns, nor is it alternating on the columns.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

Given Matrix,

$A = [\begin{matrix} a & b \\ c & d \end{matrix}]$ .

Step 2: (a) To determine F(A) = bc

F(A) = bc

Function F is linear in both columns and both rows, but it's not alternating on the columns.

Step 3: (b) To determine F(A) = cd

F(A) = cd

Function is linear in both columns, but not in both rows, nor is it alternating on the columns.

Step 4: (c) To determine F(A) = ac

$F (A) = ac$

Function is linear in both rows, but not in both columns, nor is it alternating on the columns.

Step 5: (d) To determine F(A) = bc - ad

$F (A) = bc - ad = \det A$

Function F is linear in both rows and both columns, as well as alternating on the columns.

Step 6: (e) To determine

$F (A) = c$

Function F is not linear in both rows nor both columns, nor is it alternating on the columns.

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Linear Algebra With Applications

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Short Answer

Step by Step Solution

Step 1: Given

Step 2: (a) To determine F(A) = bc

Step 3: (b) To determine F(A) = cd

Step 4: (c) To determine F(A) = ac

Step 5: (d) To determine F(A) = bc - ad

Step 6: (e) To determine

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Linear Algebra With Applications

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Short Answer

Which of the following functions F of A=[abcd] are linear in both columns? Which are linear in both rows? Which are alternating on the columns? role="math" localid="1659502796300" a. F(A)=bcb. F(A)=cdc. F(A)=acd. F(A)=bc-ade. F(A)=c

Step by Step Solution

Step 1: Given

Step 2: (a) To determine F(A) = bc

Step 3: (b) To determine F(A) = cd

Step 4: (c) To determine F(A) = ac

Step 5: (d) To determine F(A) = bc - ad

Step 6: (e) To determine

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