Matrices and determinants

A matrix with 3 rows and 2 columns has order:

• 1 3 x 3
• 2 3 x 2
• 3 6
• 4 2 x 3

What is the determinant of the matrix [[2, 3], [1, 4]]?

• 1 8
• 2 11
• 3 -5
• 4 5

If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], what is A + B?

• 1 [[1, 2], [3, 4]]
• 2 [[1, 3], [4, 4]]
• 3 [[1, 3], [4, 5]]
• 4 [[0, 2], [3, 0]]

A matrix whose determinant is zero is called:

• 1 Identity
• 2 Singular
• 3 Non-singular
• 4 Diagonal

What is the transpose of [[1, 2, 3]]?

• 1 [[3, 2, 1]]
• 2 [[1], [2], [3]]
• 3 [[1, 2, 3]]
• 4 [[0]]

What is 3 times the matrix [[1, 2], [0, 1]]?

• 1 [[3, 2], [0, 1]]
• 2 [[4, 5], [3, 4]]
• 3 [[1, 6], [0, 3]]
• 4 [[3, 6], [0, 3]]

A matrix with only one row is called a:

• 1 Row matrix
• 2 Column matrix
• 3 Square matrix
• 4 Null matrix

The identity matrix of order 2 is:

• 1 [[0, 1], [1, 0]]
• 2 [[1, 1], [1, 1]]
• 3 [[0, 0], [0, 0]]
• 4 [[1, 0], [0, 1]]

If A = [[1, 2], [3, 4]], then 2A is:

• 1 [[1, 4], [3, 8]]
• 2 [[3, 4], [5, 6]]
• 3 [[2, 4], [6, 8]]
• 4 [[2, 2], [3, 4]]

A matrix with the same number of rows and columns is:

• 1 Square
• 2 Row
• 3 Zero
• 4 Column

Two matrices can be added only if they:

• 1 Have the same determinant
• 2 Have the same order
• 3 Are square matrices
• 4 Are identity matrices

If A is 2 × 3 and B is 3 × 4, the order of AB is:

• 1 4 × 2
• 2 2 × 4
• 3 3 × 3
• 4 2 × 3

The determinant of the matrix with rows (2, 3) and (1, 4) is:

• 1 −5
• 2 8
• 3 11
• 4 5

A matrix is singular when its determinant is:

• 1 Zero
• 2 Equal to its order
• 3 One
• 4 Negative

The identity matrix of order 2 has diagonal entries:

• 1 0 and 0
• 2 1 and 0
• 3 1 and 1
• 4 2 and 2

The transpose of a matrix is formed by:

• 1 Swapping the signs of all entries
• 2 Changing rows into columns
• 3 Adding the rows
• 4 Multiplying all entries by 2

The adjoint of the matrix with rows (a, b) and (c, d) has rows:

• 1 (d, −b) and (−c, a)
• 2 (−a, −b) and (−c, −d)
• 3 (d, b) and (c, a)
• 4 (a, c) and (b, d)

If |A| = 4 and adj A is known, then A⁻¹ equals:

• 1 4 ÷ adj A
• 2 adj A − 4
• 3 adj A ÷ 4
• 4 4 × adj A

Which matrix has no inverse?

• 1 The matrix with rows (2, 4) and (1, 2)
• 2 The matrix with rows (3, 1) and (2, 1)
• 3 The matrix with rows (1, 2) and (3, 5)
• 4 The matrix with rows (1, 0) and (0, 1)