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Q1. Let f: X-Y and g: Y - Z be two functions then a. If gof: X-Z bijective function then / and g are bijective functions. b. If gof bijective function then / one-to-one and 9 onto. If gof bijective then / onto and g one-to-one. d. If one-to-one and g onto then gof bijective. Q2 Let VR be a vector space over a field R and S=((1.0.-1.0). (0.1.0.-2). (-1,0,0,1)). Then S is linearly independent and generates V b. S is linearly dependent and generates V c. S is linearly independent and does not generate V d. S is linearly dependent and does not generate V

Q1. Let f: X-Y and g: Y - Z be two functions then a. If gof: X-Z bijective function then / and g are bijective functions. b. If gof bijective function then / one-to-one and 9 onto. If gof bijective then / onto and g one-to-one. d. If one-to-one and g onto then gof bijective. Q2 Let VR be a vector space over a field R and S=((1.0.-1.0). (0.1.0.-2). (-1,0,0,1)). Then S is linearly independent and generates V b. S is linearly dependent and generates V c. S is linearly independent and does not generate V d. S is linearly dependent and does not generate V

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 34E
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Q1. Let f: X-Y and g: Y - Z be two functions then a. If gof: X-Z bijective function then / and g are bijective functions. b. If gof bijective function then / one-to-one and 9 onto. If gof bijective then / onto and g one-to-one. d. If one-to-one and g onto then gof bijective. Q2 Let VR be a vector space over a field R and S=((1.0.-1.0). (0.1.0.-2). (-1,0,0,1)). Then S is linearly independent and generates V b. S is linearly dependent and generates V c. S is linearly independent and does not generate V d. S is linearly dependent and does not generate V
Transcribed Image Text:Q1. Let f: X-Y and g: Y - Z be two functions then a. If gof: X-Z bijective function then / and g are bijective functions. b. If gof bijective function then / one-to-one and 9 onto. If gof bijective then / onto and g one-to-one. d. If one-to-one and g onto then gof bijective. Q2 Let VR be a vector space over a field R and S=((1.0.-1.0). (0.1.0.-2). (-1,0,0,1)). Then S is linearly independent and generates V b. S is linearly dependent and generates V c. S is linearly independent and does not generate V d. S is linearly dependent and does not generate V
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