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
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Chapter2: Second-order Linear Odes
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19. Prove that if {A₁, A2,..., Ak} is a linearly independent subset of
Mnxn(F), then {A₁, A½, …….‚ A£} is also linearly independent.
Transcribed Image Text:19. Prove that if {A₁, A2,..., Ak} is a linearly independent subset of Mnxn(F), then {A₁, A½, …….‚ A£} is also linearly independent.
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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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