Let V = Mnxn(F). (a) Suppose that {M1,..., Mt} C Mnxn(F) is a spanning set. Prove that {M{,.…, M£} is also a spanning set. (Hint: Express At as a linear combination of the M;'s and use transpose carefully.) (b) Prove that if B = {M11, M12, -.. , Mnn} is any basis of V, then B' = {M, M, ..., Min} is also a basis of V.

Let V = Mnxn(F). (a) Suppose that {M1,..., Mt} C Mnxn(F) is a spanning set. Prove that {M{,.…, M£} is also a spanning set. (Hint: Express At as a linear combination of the M;'s and use transpose carefully.) (b) Prove that if B = {M11, M12, -.. , Mnn} is any basis of V, then B' = {M, M, ..., Min} is also a basis of V.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.5: The Format Proof Of A Theorem

Problem 12E: Based upon the hypothesis of a theorem, do the drawings of different students have to be identical...

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