Go on. Explore!

lvl 0 • 0 xp

lvl 1

Home Market Decks Interests

MAS4105 Exam 1 T/F Practice

memorize.ai (lvl 286)

(0)

42 cards

()

Section 1

Preview this deck

If a₁x₁ + a₂x₂ + ... + aₙxₙ = 0 and x₁, x₂, ... , xₙ are linearly independent, then all the scalars ai are zero.

Front

1 / 42

Physics

0.0

0 reviews

5			0
4			0
3			0
2			0
1			0

Active users

All-time users

Favorites

Last updated

6 years ago

Date created

Mar 1, 2020

Cards (42)

Section 1

(42 cards)

If a₁x₁ + a₂x₂ + ... + aₙxₙ = 0 and x₁, x₂, ... , xₙ are linearly independent, then all the scalars ai are zero.

Front

T

Back

Every vector space contains a zero vector.

Front

T

Back

Every system of linear equations has a solution.

Front

F

Back

Suppose that V is a finite-dimensional vector space, that S₁ is a linearly independent subset of V, and that S₂ is a subset of V that generates V. Then S₁ cannot contain more vectors than S₂.

Front

T

Back

In any vector space, ax = bx implies that a = b.

Front

F

Back

If V is a vector space having dimension n, and if S is a subset of V with n vectors, then S is linearly independent if and only if S spans V.

Front

T

Back

Let W be the xy-plane in R³; that is, W = {(a₁, a₂, 0): a₁, a₂ ∈ R}. Then W = R²

Front

F

Back

If S generates the vector space V, then every vector in V can be written as a linear combination of vectors in S in only one way.

Front

F

Back

The dimension of Mmxn(F) is m+n.

Front

F

Back

Two functions in ℱ(S, F) are equal if and only if they have the same value at each element of S.

Front

T

Back

In P(F), only polynomials of the same degree may be added.

Front

F

Back

A vector space cannot have more than one basis.

Front

F

Back

In solving a system of linear equations, it is permissible to multiply an equation by any constant.

Front

F

Back

Every vector space has a finite basis.

Front

F

Back

The zero vector space has no basis.

Front

F

Back

If f and g are polynomials of degree n, then f + g is a polynomial of degree n.

Front

F

Back

Subsets of linearly dependent sets are linearly dependent.

Front

F

Back

The intersection of any two subsets of V is a subspace of V.

Front

F

Back

If V is a vector space and W is a subset of V that is a vector space, then W is a subspace of V.

Front

F

Back

If S is a subset of a vector space V, then span(S) equals the intersection of all subspaces of V that contain S.

Front

T

Back

The dimension of Pₙ(F) is n.

Front

F

Back

If f is a polynomial of degree n and c is a nonzero scalar, then cf is a polynomial of degree n.

Front

T

Back

If V is a vector space having dimension n, then V has exactly one subspace with dimension 0 and exactly one subspace with dimension n.

Front

T

Back

A vector in Fⁿ may be regarded as a matrix in Mₙx₁(F).

Front

T

Back

In any vector space, ax = ay implies that x = y.

Front

F

Back

The empty set is a subspace of every vector space.

Front

F

Back

The trace of a square matrix is the product of its diagonal entries.

Front

F

Back

The span of ∅ is ∅.

Front

F

Back

Any set containing the zero vector is linearly dependent.

Front

T

Back

A nonzero scalar of F may be considered to be a polynomial in P(F) having degree zero.

Front

T

Back

A vector space may have more than one zero vector.

Front

F

Back

In solving a system of linear equations, it is permissible to add any multiple of one equation to another.

Front

T

Back

An m x n matrix has m columns and n rows.

Front

F

Back

Every vector space that is generated by a finite set has a basis.

Front

T

Back

An n x n diagonal matrix can never have more than n nonzero entries.

Front

T

Back

Subsets of linearly independent sets are linearly independent.

Front

T

Back

If a vector space has a finite basis, then the number of vectors in every basis is the same.

Front

T

Back

If V is a vector space other than the zero vector space, then V contains a subspace W such that W ≠ V.

Front

T

Back

If S is a linearly dependent set, then each vector in S is a linear combination of other vectors in S.

Front

F

Back

The zero vector is a linear combination of any nonempty set of vectors.

Front

T

Back

Every subspace of a finite-dimensional space is finite-dimensional.

Front

T

Back

The empty set is linearly dependent.

Front

F

Back