19. Prove that if {A₁, A2,..., Ak} is a linearly independent subset ofMnxn(F), then {A₁, A½, …….‚ A£} is also linearly independent.

19. Prove that if is a linearly independent subset of , then is also linearly independent.

Answered: 19. Prove that if {A₁, A2,. Ak} is a…

19. Prove that if {A₁, A2,. Ak} is a linearly independent subset of Mnxn (F), then {(A, A₂,..., At} is also linearly independent. ...

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

19. Prove that if {A₁, A2,..., Ak} is a linearly independent subset of
Mnxn(F), then {A₁, A½, …….‚ A£} is also linearly independent.

Expert Solution

Step 1: Question Description

19. Prove that if $open curly brackets A subscript 1 comma space A subscript 2 comma.... comma A subscript k close curly brackets$ is a linearly independent subset of $M subscript n cross times n end subscript open parentheses F close parentheses$ , then $open curly brackets A subscript 1 to the power of t comma space A subscript 2 to the power of t comma... comma space A subscript k to the power of t close curly brackets$ is also linearly independent.

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