Linear Combinations of Vectors

Linear Combinations of Vectors

12th Grade

13 Qs

quiz-placeholder

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Linear Combinations of Vectors

Linear Combinations of Vectors

Assessment

Quiz

Mathematics

12th Grade

Hard

Created by

Anthony Clark

Used 1+ times

FREE Resource

13 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

Option (a)

Option (b)

Option (c)

Option (d)

2.

FILL IN THE BLANK QUESTION

1 min • 1 pt

The linear span L(S) of any subset S of a vector space V(F) is a .........of V(F).

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

In a vector space of dimension 5, a subset A containing 6 elements is generating set. Then

A is Linearly independent also.

There is one element in A which can be written as a linear combination of others.

A contains zero element

Can not say anything about the set A

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

If W is a subspace of a vector space V(F) and α, β ∈ W then for any scalar c ..........

cα + β ∈ V

cα + β ∈ W

cα + β ∉ V

cα + β ∉ W

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Is the vectors (1, 2, 3), (4, 5, 6) and (7, 8, 9) span the vector

space ℝ3.

yes

no

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Let V be a vector space, and let W be a subset of V. What does it mean when we say that is linearly independent?

S is closed under both addition and scalar multiplication.

The only way to write 0 as a linear combination of elements of S.

All the elements of are distinct from each other.

S has nullity zero.

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Let V be a five-dimensional vector space, and let S be a subset of V which spans V . Then S

Must have exactly five elements.

Must consist of at least five elements.

Must have infinitely many elements.

Must have at most five elements.

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