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-8 (a) If A =} 4 4 7 1 -8 4, , prove that A- = A' where A' is the transpose of A. (- (b) Show that the set Fmxn of all m x n matrices over a field F is a vector space over F with respect to the addition of matrices as vector addition and multiplication of a (8 matrix by a scalar as scalar multiplication.

-8 (a) If A =} 4 4 7 1 -8 4, , prove that A- = A' where A' is the transpose of A. (- (b) Show that the set Fmxn of all m x n matrices over a field F is a vector space over F with respect to the addition of matrices as vector addition and multiplication of a (8 matrix by a scalar as scalar multiplication.

Advanced Engineering Mathematics
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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-8 1 (a) If A = } , prove that A¬! = A' where A' is the transpose of A. 4 4 7 1 -8 4 (b) Show that the set Fmxn of all m x n matrices over a field F is a vector space over F with respect to the addition of matrices as vector addition and multiplication of a (8 matrix by a scalar as scalar multiplication.
Transcribed Image Text:-8 1 (a) If A = } , prove that A¬! = A' where A' is the transpose of A. 4 4 7 1 -8 4 (b) Show that the set Fmxn of all m x n matrices over a field F is a vector space over F with respect to the addition of matrices as vector addition and multiplication of a (8 matrix by a scalar as scalar multiplication.
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