A) The complex numbers is a 2-dimensional R-vector space. B) The set of invertible 2 × 2 matrices with entries from R is a subspace of M2(R). C) If T : V → W is a linear transformation, then it is always true that T (0V ) = 0W
A) The complex numbers is a 2-dimensional R-vector space. B) The set of invertible 2 × 2 matrices with entries from R is a subspace of M2(R). C) If T : V → W is a linear transformation, then it is always true that T (0V ) = 0W
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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Question
Answer True or False
A) The
B) The set of invertible 2 × 2 matrices with entries from R is a subspace
of M2(R).
C) If T : V → W is a linear transformation, then it is always true that
T (0V ) = 0W
D) The zero vector is always an eigenvector for a linear transformation.
E) If X ⊕ Y = X ⊕ Z then Y = Z.
F) If a function f : X → Y is surjective, then there exists g : Y → X such that f ◦ g = idY .
G) If U and W are subspaces of V, then U ∪ W is a subspace of V.
H) ⟨T,v⟩ is always a T-invariant subspace of V ( v ∈ V ).
I) For any linear transformation T : V → V , ker(T ) ≤ ker(T2).
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