Matrices: Comprehensive Learning Quizzes for Advanced Diploma in Healthcare

Question 1

Which of the following is the correct representation of a matrix?

Accepted Answer

[[a, b], [c, d]]

Answer

[a, b]

Answer

[a b]

Answer

[a | b]

Question 2

What is the determinant of the matrix [[2, 3], [4, 5]]?

Accepted Answer

10

Answer

-2

Answer

2

Answer

-10

Question 3

How are matrices commonly utilized in healthcare?

Accepted Answer

For all of the above purposes

Answer

To model drug interactions

Answer

To represent patient data

Answer

To analyze medical images

Question 4

Which of the following is NOT a characteristic of matrices?

Accepted Answer

Matrices can always be inverted

Answer

Matrices can be added and subtracted if they have equal dimensions

Answer

Matrices can be multiplied by scalars

Answer

Matrices have determinants

Question 5

Which operation cannot be performed on matrices?

Accepted Answer

Dividing two matrices

Answer

Adding two matrices

Answer

Multiplying a matrix by a scalar

Answer

Finding the transpose of a matrix

Question 6

Which of the following is not a type of matrix?

Accepted Answer

Vector

Answer

Diagonal matrix

Answer

Unit matrix

Answer

Symmetric matrix

Question 7

Which of the following operations cannot be performed on matrices?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 8

Which property of matrices states that the order in which matrices are multiplied matters?

Accepted Answer

Commutative property

Answer

Associative property

Answer

Distributive property

Answer

Multiplicative identity property

Question 9

What are the dimensions of the matrix C = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?

Accepted Answer

3x3

Answer

2x3

Answer

3x2

Answer

2x2

Question 10

Which of the following matrices is a diagonal matrix?

Accepted Answer

[[1, 0], [0, 1]]

Answer

[[1, 2], [3, 4]]

Answer

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

Answer

[[1, 2, 3], [4, 0, 5], [6, 7, 8]]

Question 11

Find the adjoint of the matrix A = [[2, 1], [-1, 3]]

Accepted Answer

[[3, -1], [1, 2]]

Answer

[[3, 1], [1, 2]]

Answer

[[3, -1], [-1, 2]]

Answer

[[3, 1], [-1, 2]]

Question 12

Which of the following is NOT an elementary matrix operation?

Accepted Answer

Determinant calculation

Answer

Row swap

Answer

Column multiplication

Answer

Row addition

Question 13

What is the transpose of the matrix [[2, 3, 4], [5, 6, 7]]?

Accepted Answer

[[2, 5], [3, 6], [4, 7]]

Answer

[[2, 3, 4], [5, 6, 7]]

Answer

[[4, 3, 2], [7, 6, 5]]

Answer

[[7, 6, 5], [4, 3, 2]]

Question 14

Which of the following is NOT a type of elementary matrix?

Accepted Answer

Adjugate matrix

Answer

Row swap matrix

Answer

Column multiply matrix

Answer

Zero row matrix

Question 15

Which of the following is not a fundamental operation that can be performed with matrices?

Accepted Answer

Exponentiation

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 16

For matrices A = [a b] and B = [c d], what is the determinant of the matrix AB?

Accepted Answer

ad - bc

Answer

ac - bd

Answer

-ad + bc

Answer

-ac + bd

Question 17

Which of the following matrices cannot be inverted?

Accepted Answer

[0 0]

Answer

[1 2]

Answer

[1 0]

Answer

[0 1]

Question 18

Given matrices A = [a b] and B = [c d], what is the trace of the matrix AB?

Accepted Answer

a + d

Answer

a - d

Answer

c + b

Answer

c - b

Question 19

Which of the following is not a potential limitation of using matrices in healthcare?

Accepted Answer

Enhances communication and teamwork among healthcare professionals

Answer

May not capture all relevant patient information

Answer

Can be challenging to analyze extensive and intricate matrices

Answer

Requires specific software or tools

Question 20

Which operation transforms a matrix into its transpose?

Accepted Answer

Interchanging its rows and columns

Answer

Multiplying it by its inverse

Answer

Adding its identity matrix

Answer

Taking its determinant

Question 21

In MRI scans, technicians use transformation matrices to manipulate images. How can the inverse matrix be used to restore the original image?

Accepted Answer

Multiply the transformed image by the inverse matrix

Answer

Add the transformed image to the inverse matrix

Answer

Subtract the inverse matrix from the transformed image

Answer

Raise the transformed image to the power of the inverse matrix

Question 22

Which of the following operations cannot be performed on matrices?

Accepted Answer

Multiplication by vectors

Answer

Inversion

Answer

Multiplication by scalars

Answer

Addition and subtraction

Question 23

What are the dimensions of a matrix with 5 rows and 3 columns?

Accepted Answer

5 x 3

Answer

15 x 8

Answer

6 x 10

Answer

3 x 5

Question 24

Which of the following operations involves performing the same operation on each element of two matrices?

Accepted Answer

Element-wise operation

Answer

Determinant calculation

Answer

Matrix multiplication

Answer

Matrix inversion

Question 25

Which of the following matrix types has all elements on the diagonal equal to 1 and all other elements equal to 0?

Accepted Answer

Identity matrix

Answer

Orthogonal matrix

Answer

Symmetric matrix

Answer

Triangular matrix

Question 26

Indicate which of the following matrices is invertible.

Accepted Answer

[[2, 1], [3, 4]]

Answer

[[2, 1], [3, 3]]

Answer

[[1, 2], [2, 4]]

Answer

[[0, 1], [0, 0]]

Question 27

Determine the product of matrices [[1, 2], [3, 4]] and [[5, 6], [7, 8]]

Accepted Answer

[[19, 22], [43, 50]]

Answer

[[25, 30], [45, 60]]

Answer

[[5, 6], [7, 8]]

Answer

[[1, 2], [3, 4]]

Question 28

Identify an application of matrices in the healthcare context.

Accepted Answer

Modeling the spread of infectious diseases

Answer

Finding the area of a triangle

Answer

Solving quadratic equations

Answer

Calculating the volume of a sphere

Question 29

Identify a singular matrix.

Accepted Answer

[[1, 0], [0, 0]]

Answer

[[1, 2], [3, 4]]

Answer

[[1, 0], [0, 1]]

Answer

[[2, 1], [1, 2]]

Question 30

Which of the following is a property of matrices?

Accepted Answer

Matrices can be multiplied by both scalars and other matrices

Answer

Matrices can be added and subtracted only if they have different dimensions

Answer

The determinant of a matrix is always positive

Answer

Matrices cannot be transposed

Question 31

Which of the following is not an operation that can be performed on matrices?

Accepted Answer

Division

Answer

Subtraction

Answer

Addition

Answer

Multiplication

Question 32

A hospital has 40 beds in its general ward and 30 beds in its maternity ward. This information can be represented as a matrix [[40], [30]]. What is the sum of the elements in this matrix?

Accepted Answer

70

Answer

10

Answer

1200

Answer

40

Question 33

Which of the following is an identity matrix of order 2?

Accepted Answer

[[1, 0], [0, 1]]

Answer

[[0, 1], [1, 0]]

Answer

[[0, 0], [0, 0]]

Answer

[[1, 1], [1, 1]]

Question 34

Which of the following statements about matrix multiplication is NOT true?

Accepted Answer

The product of two matrices always has the same order as the original matrices.

Answer

The order of multiplication matters (AB is not always equal to BA).

Answer

The product of two matrices may not be defined if the number of columns in the first matrix does not equal the number of rows in the second matrix.

Question 35

The trace of a matrix is the sum of its:

Accepted Answer

Diagonal elements

Answer

Elements above the main diagonal (superdiagonal)

Answer

Elements below the main diagonal (subdiagonal)

Answer

Elements not on the main diagonal (off-diagonal)

Question 36

A hospital uses a matrix to represent the number of patients in different wards. What does each individual entry (or element) in this matrix represent?

Accepted Answer

The number of patients in a specific ward.

Answer

The patient's medical history.

Answer

The type of ward.

Answer

The doctor assigned to the ward.

Question 37

Given matrices A = [2 3] and B = [1 4], what is the result of adding these matrices (A + B)?

Accepted Answer

[3 7]

Answer

[3 4]

Answer

[2 12]

Answer

It is not possible to add these matrices because they have different dimensions.

Question 38

A pharmacy tracks medication inventory using matrices. If matrix A represents the stock on Monday and matrix B represents the stock sold on Tuesday, what matrix operation would you use to calculate the remaining stock on Tuesday?

Accepted Answer

A - B

Answer

A * B

Answer

A + B

Answer

B - A

Question 39

A matrix has 3 rows and 2 columns. What is the order (or dimension) of this matrix?

Accepted Answer

3 x 2

Answer

3 + 2

Answer

2 x 3

Answer

6

Question 40

What is the determinant of the matrix C = [4 2; 1 3]?

Accepted Answer

10

Answer

11

Answer

-2

Answer

14

Question 41

If the determinant of a matrix is zero, what can you conclude about its inverse?

Accepted Answer

The inverse does not exist.

Answer

The inverse is the same as the original matrix.

Answer

The inverse is a zero matrix.

Answer

The inverse can be any matrix.

Question 42

Which of the following is NOT a property of matrix multiplication?

Accepted Answer

Commutative Property (A * B = B * A)

Answer

Distributive Property (A * (B + C) = A * B + A * C)

Answer

Identity Property (A * I = A, where I is the identity matrix)

Answer

Associative Property (A * (B * C) = (A * B) * C)

Question 43

A hospital uses a transition matrix to model patient movement between wards. What do the elements in this matrix represent?

Accepted Answer

The probability of a patient moving from one ward to another.

Answer

The number of patients in each ward.

Answer

The time spent by a patient in each ward.

Question 44

Which matrix operation is used to solve a system of linear equations using matrices?

Accepted Answer

Finding the inverse of the coefficient matrix.

Answer

Multiplying the coefficient matrix by a scalar.

Answer

Calculating the determinant of the augmented matrix.

Answer

Transposing the coefficient matrix.

Question 45

A study analyzes the effectiveness of two different treatments using a matrix. What might the rows and columns represent in this context?

Accepted Answer

Rows: Treatment groups, Columns: Outcome measures

Answer

Rows: Medication type, Columns: Dosage

Answer

Rows: Hospital wards, Columns: Number of doctors

Answer

Rows: Patient age, Columns: Treatment cost