AMAI Quiz (24-25)

If two vectors are orthogonal, their dot product is:

a) 1

b) -1

c) 0

d) Infinity

• a

• b

• c

• d

A unit vector has a magnitude of:

a) 0

b) 1

c) Infinity

d) Any value

• a

• b

• c

• d

The transpose of a matrix is obtained by:

a) Swapping rows and columns

b) Multiplying by -1

c) Rotating by 360 degrees

d) Taking the inverse

• a

• b

• c

• d

The trace of a square matrix is the sum of its:

a) First column elements

b) Diagonal elements

c) All elements

d) First row elements

• a

• b

• c

• d

A matrix is orthogonal if:

a) Aᵀ = A⁻¹

b) Aᵀ = A

c) A = -Aᵀ

d) A = 0

• a

• b

• c

• d

An eigenvector of a matrix A satisfies the equation:

a) Ax = λx

b) Ax = x/λ

c) Ax = 0

d) Ax = -λx

• a

• b

• c

• d

Eigenvalues can be:

a) Real

b) Complex

c) Both real and complex

d) Only integers

• a

• b

• c

• d

The product of the eigenvalues of a matrix is equal to its:

a) Trace

b) Determinant

c) Rank

d) Nullity

• a

• b

• c

• d

SVD decomposes a matrix A into:

a) A = ULVᵀ

b) A = UΣVᵀ

c) A = LU

d) A = QR

• a

• b

• c

• d

In SVD, Σ is a:

a) Diagonal matrix of singular values

b) Orthogonal matrix

c) Unitary matrix

d) Null matrix

• a

• b

• c

• d