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Properties of the Transpose In Problems 39–42, either prove the properties in general using the fact that [ a, ]T = [a, ). or demonstrate the properties for general 3 × 3 matrices. 39. (A")T = A 40. (A + B)T = AT + BT 41. (kA) = kAT, for any scalar k 42. (AB)" = BTAT

Properties of the Transpose In Problems 39–42, either prove the properties in general using the fact that [ a, ]T = [a, ). or demonstrate the properties for general 3 × 3 matrices. 39. (A")T = A 40. (A + B)T = AT + BT 41. (kA) = kAT, for any scalar k 42. (AB)" = BTAT

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Properties of the Transpose In Problems 39–42, either prove the properties in general using the fact that [ a, ]T = [a, ). or demonstrate the properties for general 3 × 3 matrices. 39. (A")T = A 40. (A + B)T = AT + BT 41. (kA) = kAT, for any scalar k 42. (AB)" = BTAT
Transcribed Image Text:Properties of the Transpose In Problems 39–42, either prove the properties in general using the fact that [ a, ]T = [a, ). or demonstrate the properties for general 3 × 3 matrices. 39. (A")T = A 40. (A + B)T = AT + BT 41. (kA) = kAT, for any scalar k 42. (AB)" = BTAT
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