Matrix and Determinant Quiz

If a matrix has a row of all zeros, what is its determinant?

• 1

• -1

• 0

• It depends on the other rows

A square matrix is singular if its determinant is:

• 1

• -1

• 0

• any non-zero number

Given vectors u = (1, 2, 3) and v = (4, 5, 6), find a linear combination au + bv = (0, 0, 0), where a and b are not both zero.

• a = 0, b = 0

• a = 1, b = -1

• a = 2, b = -1

• a = 3, b = -2

What is the dimension of the vector space of all 3x3 matrices?

• 3

• 6

• 9

• Infinite

If A is a 2x2 matrix with det(A) = 7, then det(A⁻¹) = ?

• 7

• 1/7

• -7

• 0

What happens to the determinant of a matrix if you add a multiple of one row to another?

• It is multiplied by that multiple.

• It changes sign.

• It is unchanged.

• It is divided by that multiple.

If the vectors u = (1, 2, 3) and v = (k, 6, 9) are linearly dependent, what is k?

• 2

• 3

• 4

• 6

What is the size of the matrix product of a 2x3 matrix and a 3x4 matrix?

• 2x3

• 3x4

• 2x4

• 3x3

If A is an idempotent matrix (A² = A), what is one possible eigenvalue of A?

• 2

• 1

• -1

• 0

A matrix is nilpotent if:

• A² = A

• Aᵀ = A

• Aᵏ = 0 for some positive integer k

• det(A) = 0