Explanation Given: The matrix is, A = [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] Approach: To encode a message multiply un-coded row matrices by encoding matrix A to obtain coded row matrices. [ Uncoded Matrix ] [ Encoding Matrix ] = [ Coded Matrix ] Calculation: Use 1 for A , 2 for B , 3 for C and so on. Make group of three alphabets to produce un-coded row matrices of order 1 × 3 as shown below. [ 11 14 15 ] [ 3 11 0 ] [ 15 14 0 ] [ 23 15 15 ] [ 4 0 0 ] K N O C K O N W O O D To encode a message multiply un-coded row matrices by encoding matrix A to obtain coded row matrices. [ Uncoded Matrix ] [ Encoding Matrix ] = [ Coded Matrix ] So, [ 11 14 15 ] [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] = [ 11 + 14 + 90 − 11 + 0 − 30 0 − 14 − 45 ] = [ 115 − 41 − 59 ] And, [ 3 11 0 ] [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] = [ 3 + 11 + 0 − 3 + 0 + 0 0 − 11 + 0 ] = [ 14 − 3 − 11 ] And, [ 15 14 0 ] [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] = [ 15 + 14 + 0 − 15 + 0 + 0 0 − 14 + 0 ] = [ 29 − 15 − 14 ] And, [ 23 15 15 ] [ 1 − 1 0 1 0 − 1 6 − 2 − 3 ] = [ 23 + 15 + 90 − 23 + 0 − 30 0 − 15 − 45 ] = [ 128 − 53 − 60 ] And,

Bundle: Precalculus, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's Precalculus, 10th Edition, Single-Term

10th Edition

ISBN: 9781337605090

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 8.CT, Problem 15CT

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The uncoded 1×3 row matrices for the message “KNOCK ON WOOD” and then encode the message using the encoding matrix A.

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Chapter 8.CT, Problem 14CT

Chapter 8.CT, Problem 16CT

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Bundle: Precalculus, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's Precalculus, 10th Edition, Single-Term

Ch. 8.1 - Prob. 1CP Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 5CP Ch. 8.1 - Prob. 6CP Ch. 8.1 - Prob. 7CP Ch. 8.1 - Prob. 8CP Ch. 8.1 - Prob. 9CP Ch. 8.1 - Prob. 1E

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The uncoded 1 × 3 row matrices for the message “KNOCK ON WOOD” and then encode the message using the encoding matrix A .

Solution Summary: The author explains how to encode a message by multiplying un-coded row matrices by encoding matrix A.

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To write:

The uncoded 1×3 row matrices for the message “KNOCK ON WOOD” and then encode the message using the encoding matrix A.

Want to see the full answer?

Chapter 8 Solutions

The uncoded 1 × 3 row matrices for the message “KNOCK ON WOOD” and then encode the message using the encoding matrix A .

Solution Summary: The author explains how to encode a message by multiplying un-coded row matrices by encoding matrix A.

Concept explainers

Videos

To write: The uncoded 1×3 row matrices for the message “KNOCK ON WOOD” and then encode the message using the encoding matrix A.

Want to see the full answer?

Chapter 8 Solutions

To write:

The uncoded 1×3 row matrices for the message “KNOCK ON WOOD” and then encode the message using the encoding matrix A.