Determine whether the following statements are True or False:   (a) There is no injective linear transformation from R3 to R2.   (b) Fixed two real numbers, m and b, consider the set of vectors of R2 given by ℓ = {(x, y) ∈ R2 | y = mx + b}, that is, vectors starting from the origin and ending on the line with slope m that intersects the y-axis at b. Then ℓ is not a vector subspace of

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 11CM
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Determine whether the following statements are True or False:
 
(a) There is no injective linear transformation from R3 to R2.
 
(b) Fixed two real numbers, m and b, consider the set of vectors of R2 given by ℓ = {(x, y) ∈ R2 | y = mx + b}, that is, vectors starting from the origin and ending on the line with slope m that intersects the y-axis at b. Then is not a vector subspace of R2, regardless of the values ​​of m and b.
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