BMath Bachelor of Mathematics Linear Algebra and Matrix Theory

Question 1

What is the determinant of the 2×2 matrix [[a, b], [c, d]]?

Accepted Answer

ad − bc

Answer

ac − bd

Answer

ab − cd

Answer

a + d

Question 2

A square matrix A is invertible if and only if:

Accepted Answer

Its determinant is non-zero

Answer

Its trace is non-zero

Answer

All its entries are positive

Answer

It is symmetric

Question 3

What is the rank of a matrix?

Accepted Answer

The dimension of its column space

Answer

The number of rows

Answer

The number of non-zero entries

Answer

Its largest eigenvalue

Question 4

If λ is an eigenvalue of matrix A with eigenvector v, which equation must hold?

Accepted Answer

Av = λv

Answer

Av = λI

Answer

A + λI = 0

Answer

λA = v

Question 5

The null space of a matrix A consists of:

Accepted Answer

All vectors x such that Ax = 0

Answer

All vectors b such that Ax = b has a solution

Answer

All eigenvalues of A

Answer

The set of pivot columns of A

Question 6

A set of vectors {v₁, v₂, …, vₙ} is linearly independent if:

Accepted Answer

c₁v₁ + c₂v₂ + … + cₙvₙ = 0 implies all cᵢ = 0

Answer

Each vector is a unit vector

Answer

No vector is the zero vector

Answer

The vectors are mutually orthogonal