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If the map f:R4-R3 is defined by f (x, y, z, w) = ( w – x , z, y) then which of the following is true? A. Kerf = { (a,0,0,a) la E R} B. The map is injective. C. The map s is not a linear map. D. The map s is an isomorphism.

If the map f:R4-R3 is defined by f (x, y, z, w) = ( w – x , z, y) then which of the following is true? A. Kerf = { (a,0,0,a) la E R} B. The map is injective. C. The map s is not a linear map. D. The map s is an isomorphism.

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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A Moving to another question will save this response. « < Question 5 of 46 > » Question 5 Answer If the map f:R4→R3 Is defined by f(x, y,z,w) = ( w – x.z.v) then which of the following is true? A. Kerf = { (a,0,0,a) la E R} B. The map f is injective. C. The map s is not a linear map. D. The map f is an isomorphism.
Transcribed Image Text:A Moving to another question will save this response. « < Question 5 of 46 > » Question 5 Answer If the map f:R4→R3 Is defined by f(x, y,z,w) = ( w – x.z.v) then which of the following is true? A. Kerf = { (a,0,0,a) la E R} B. The map f is injective. C. The map s is not a linear map. D. The map f is an isomorphism.
A Moving to another question will save this response. < Question 7 of 46 > > Question 7 swer Let B={v,,v,..v and s={u ,,u,....,u_} be two bases of a vector space y over a field F. Which of the following is correct? А. is still a basis of v. В. Since and s are both linearly independent, no vector in B can be written as a linear combination of the B S vectors in s. C. The union"BUS' is also a basis of v. D. None of the choices in the list is correct.
Transcribed Image Text:A Moving to another question will save this response. < Question 7 of 46 > > Question 7 swer Let B={v,,v,..v and s={u ,,u,....,u_} be two bases of a vector space y over a field F. Which of the following is correct? А. is still a basis of v. В. Since and s are both linearly independent, no vector in B can be written as a linear combination of the B S vectors in s. C. The union"BUS' is also a basis of v. D. None of the choices in the list is correct.
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