Let B be a subset of R4. Which of the following statements are correct?If |B| = 5, then B is not linearly independent.If |B| = 5, then B spans R4If |B| = 3, then B does not span R4If B is a base, then |B| = 4.If |B| = 3, then B is linearly independent.

Answer Option (1) We know that, dimension of R4 is 4. But here given B is a subset of R4 and |B| =…

Answered: Let B be a subset of R4. Which of the…

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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5. For which real values of 1 do the following vectors form a linearly independent set in R³?
a +c b+c b) h(a + bx + ca²) = 1+b+c Is this mapping linear?
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Recall the definition of Linear Independence: The set {V1,..., Vn} is linearly independent if, whenever a₁ V₁ +...+ an Vn = 0, it must be that a₁ = = an = 0. Suppose that {v2, V3} is linearly independent. Briefly describe what is wrong with the following "proof" that {V1, V2, V3} is linearly independent (where V₁ is some nonzero vector): Since (v2, V3} is linearly independent, a2V2 + α3 V3 = 0. Then, if a₁V₁ + a2 V2 + a3 V3 = 0, we have that a₁ V₁ +0=0 so that a₁ = 0. Therefore, {V1, V2, V3} is linearly independent.
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Let B be a subset of R4. Which of the following statements are correct? If |B| = 5, then B is not linearly independent. If |B| = 5, then B spans R4 If IBI = 3, then B does not span R4 If B is a base, then |B| = 4. If |B| = 3, then B is linearly independent.