APM3715 Assessment 2 (Project) Answers Year 2025 Span - correct answer-The set of all linear combinations x₁u₁ + ... + xₙuₙ, where x₁, ..., xₙ can be any real numbers. Linear Independence - correct answer-The only solution to the vec

APM3715 Assessment 2 (Project) Answers Year
2025




Span - correct answer-The set of all linear
combinations x₁u₁ + ... + xₙuₙ, where x₁, ..., xₙ can
be any real numbers.

Linear Independence - correct answer-The only
solution to the vector equation x₁u₁ + ... + xₙuₙ = 0
is the trivial solution.

Linearly Dependent - correct answer-If a set of
vectors contains the zero vector, is the set linearly
dependent or independent?

Linearly Dependent - correct answer-If an nxm set
of vectors in Rⁿ exists such n < m, is the set
linearly dependent or independent?

Linearly Dependent - correct answer-If one of the
vectors in a set of vectors is a linear combination
of one of the other vectors, is the set linearly
dependent or independent?

, Ax = {0} - correct answer-General Form of a
Homogeneous Linear System

1. Closed under addition, 2. Closed under scalar
multiplication - correct answer-Conditions
Required to Form a Transformation

One-to-One - correct answer-Let T be a linear
transformation defined by T(x) = Ax. The columns
of A are linearly independent.

Onto - correct answer-Let T be a linear
transformation defined by T(x) = Ax. The columns
of A span Rⁿ.

One-to-One - correct answer-Let T be a linear
transformation. T(x) ={0} has only the trivial
solution x = {0}.

1. Contains the zero vector, 2. Closed under
addition, 3. Closed under scalar multiplication -
correct answer-Conditions Required to Form a
Subspace

Yes - correct answer-Is a span a subspace?