TRUE or FALSE 1. The set R³, with the vector addition operation defined by (a1, a2, as) (b₁,b2, bz) = (a₁ + b₁ + 5, a2 + b₂ −7, a3 + b3 + 1) defined by and scalar multiplication co (a1, a2, a3) = (ca₁ +5(e-1), ca2-7(c-1), ca3 +c-1). 2. The set of vectors {(a,b) € R²} with scalar multiplication defined by k(a, b) = (ka, 0) is a vector space. 000 a basis for R³? a. Yes, because it spans R3 b. No, because it does not span R3. c. Yes, because it is linearly independent. d. No, because it is not linearly independent. Choose the correct answer: 3. Is
TRUE or FALSE 1. The set R³, with the vector addition operation defined by (a1, a2, as) (b₁,b2, bz) = (a₁ + b₁ + 5, a2 + b₂ −7, a3 + b3 + 1) defined by and scalar multiplication co (a1, a2, a3) = (ca₁ +5(e-1), ca2-7(c-1), ca3 +c-1). 2. The set of vectors {(a,b) € R²} with scalar multiplication defined by k(a, b) = (ka, 0) is a vector space. 000 a basis for R³? a. Yes, because it spans R3 b. No, because it does not span R3. c. Yes, because it is linearly independent. d. No, because it is not linearly independent. Choose the correct answer: 3. Is
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please answer 1 to 3
Transcribed Image Text:TRUE or FALSE
1. The set R³, with the vector addition operation defined by
(a1, a2, as) (b₁,b2, bz) = (a1 + b₁ + 5, a₂ + b₂ −7, a3 + b3 + 1)
defined by
and scalar multiplication
co (a1, 02, 03) = (ca₁ +5(c-1), ca₂-7(c-1), caz+c-1).
2.
The set of vectors {(a, b) € R²} with scalar multiplication defined by k(a, b) = (ka, 0)
is a vector space.
900
} a basis for R³?
a. Yes, because it spans R3
b. No, because it does not span R3.
c. Yes, because it is linearly independent.
d. No, because it is not linearly independent.
Choose the correct answer:
3.
Is {
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