Properties of the Transpose In Problems 39–42, either provethe properties in general using the fact that [ a, ]T = [a, ).or demonstrate the properties for general 3 × 3 matrices.39. (A")T = A40. (A + B)T = AT + BT41. (kA) = kAT, for any scalar k42. (AB)" = BTAT

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 3AEXP

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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