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R³ R³ We consider the linear map f(x,y,z)+(-x+y+z,x-y+z,x-y-32) (1) Determine the kernel of f. (2) Is f injective? Bijective? (3) Write the matrix B of f in the canonical basis of R³.

R³ R³ We consider the linear map f(x,y,z)+(-x+y+z,x-y+z,x-y-32) (1) Determine the kernel of f. (2) Is f injective? Bijective? (3) Write the matrix B of f in the canonical basis of R³.

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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EXERCISE 2: LINEAR MAP AND DETERMINANT R³ → R³ We consider the linear map f(x, y, z) → (-x+y+z₁x−y+z₁x − y − 3z) (1) Determine the kernel of f. (2) Is f injective? Bijective? (3) Write the matrix B of f in the canonical basis of R³. (4) For which values of ß the vector v = (1,1, ß) belong to Im(f)?
Transcribed Image Text:EXERCISE 2: LINEAR MAP AND DETERMINANT R³ → R³ We consider the linear map f(x, y, z) → (-x+y+z₁x−y+z₁x − y − 3z) (1) Determine the kernel of f. (2) Is f injective? Bijective? (3) Write the matrix B of f in the canonical basis of R³. (4) For which values of ß the vector v = (1,1, ß) belong to Im(f)?
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