Matrix and Determinant - Practice Questions

• In this set of practice questions, we will be covering topics related to matrices and determinants.
• We will go through different types of problems and learn methods to solve them efficiently.
• Make sure to understand basic matrix operations and properties of determinants before attempting these questions.

Question 1

• Given a matrix A as follows: A = [1 3 5] [2 4 6] [7 8 9]
• Find the determinant of matrix A.

Question 2

• Given matrices A and B as follows: A = [2 3] [4 5] B = [1 2] [3 4]
• Calculate the matrix product of A and B.

Question 3

• Solve the following system of equations using matrices: [3x + 2y = 8] [x - 4y = -1]

Question 4

• Given matrix A as follows: A = [3 -1] [2 4]
• Find the inverse of matrix A, if it exists.

Question 5

• Find the adjoint of the matrix A: A = [1 2 1] [0 1 3] [1 2 2]

Question 6

• Solve the following system of equations using Cramer’s rule: [2x + 3y = 7] [4x - 2y = 2]

Question 7

• Given matrix A as follows: A = [2 1 0] [4 5 -1] [6 7 3]
• Calculate the rank of matrix A.

Question 8

• Given matrix A as follows: A = [1 2 4] [3 6 9]
• Determine whether matrix A is singular or non-singular.

Question 9

• Compute the eigenvalues and eigenvectors for the matrix A: A = [4 2] [1 3]

Question 10

• Find the solution to the following system of equations using matrix inversion method: [2x + y = 5] [4x + 3y = 11] Please solve these questions individually and we will discuss the solutions in the next set of slides.

Matrix and Determinant - Practice Questions

• Question 1
  • Given matrix A as follows: A = [1 3 5] [2 4 6] [7 8 9]
  • Find the determinant of matrix A.
• Question 2
  • Given matrices A and B as follows: A = [2 3] [4 5] B = [1 2] [3 4]
  • Calculate the matrix product of A and B.
• Question 3
  • Solve the following system of equations using matrices: [3x + 2y = 8] [x - 4y = -1]

Matrix and Determinant - Practice Questions

• Question 4
  • Given matrix A as follows: A = [3 -1] [2 4]
  • Find the inverse of matrix A, if it exists.
• Question 5
  • Find the adjoint of the matrix A: A = [1 2 1] [0 1 3] [1 2 2]
• Question 6
  • Solve the following system of equations using Cramer’s rule: [2x + 3y = 7] [4x - 2y = 2]

Matrix and Determinant - Practice Questions

• Question 7
  • Given matrix A as follows: A = [2 1 0] [4 5 -1] [6 7 3]
  • Calculate the rank of matrix A.
• Question 8
  • Given matrix A as follows: A = [1 2 4] [3 6 9]
  • Determine whether matrix A is singular or non-singular.
• Question 9
  • Compute the eigenvalues and eigenvectors for the matrix A: A = [4 2] [1 3]

Matrix and Determinant - Practice Questions

• Question 10
  • Find the solution to the following system of equations using matrix inversion method: [2x + y = 5] [4x + 3y = 11]
• Question 11
  • Given the matrix A: A = [1 0 0] [0 2 0] [0 0 3] Find the rank, determinant, and eigenvalues of matrix A.
• Question 12
  • Solve the following system of equations using matrices: [3x + 2y + 4z = 12] [x - 2y + z = 1] [2x + y + 3z = 7]

Matrix and Determinant - Practice Questions

• Question 13
  • Given matrix A as follows: A = [1 2] [3 4]
  • Compute A^2 - 2A + 3I, where I is the identity matrix.
• Question 14
  • Calculate the determinant of the matrix A: A = [4 1 3] [2 5 2] [1 0 2]
• Question 15
  • Solve the following system of equations: [2x - y + 3z = 7] [4x + 2y - z = 1] [3x + 4y + 2z = 10]

Matrix and Determinant - Practice Questions

• Question 16
  • Given matrix A as follows: A = [2 -1 5] [3 0 -4] [1 2 -1]
  • Find the eigenvalues and eigenvectors of matrix A.
• Question 17
  • Determine whether the vectors [(2, -1, 3)] and [(4, -2, 6)] are linearly independent or not.
• Question 18
  • Find the inverse of the matrix A: A = [1 2 1] [0 1 3] [2 2 1]

Matrix and Determinant - Practice Questions

• Question 19
  • Solve the following system of equations: [x + 2y + 3z = 1] [2x - y + 5z = 2] [3x + 4y - z = 0]
• Question 20
  • Given matrix A as follows: A = [2 4 -1] [-1 -2 3] [3 6 -5]
  • Calculate A^2 and A^3.

Matrix and Determinant - Practice Questions

• Question 21
  • Find the determinant of the matrix A: A = [3 -2 1] [4 0 -3] [1 2 1]
• Question 22
  • Solve the following system of equations: [x + y - z = 6] [2x + 3y + z = 7] [3x - y + 4z = 9]
• Question 23
  • Given matrix A as follows: A = [2 -1 4] [1 3 -2] [3 2 1]
  • Find the adjoint of matrix A.

Matrix and Determinant - Practice Questions

• Question 24
  • Calculate the product of matrices A and B: A = [1 2] [3 4] B = [5 6] [7 8]
• Question 25
  • Find the inverse of the matrix A: A = [3 -2] [4 -5]
• Question 26
  • Solve the following system of equations: [2x + y - z = 0] [3x - 2y + z = 5] [x + 3y - 2z = 6]

Matrix and Determinant - Practice Questions

• Question 27
  • Given matrix A as follows: A = [1 -2 3] [5 4 -1] [-2 3 6]
  • Determine whether matrix A is symmetric or not.
• Question 28
  • Find the eigenvalues and eigenvectors of the matrix A: A = [2 3 1] [0 1 2] [3 4 2]
• Question 29
  • Solve the following system of equations: [3x + 2y + 4z = 12] [x - 2y + z = 1] [2x + y + 3z = 7]

Matrix and Determinant - Practice Questions

• Question 30
  • Given matrix A as follows: A = [2 -1] [3 0]
  • Find the determinants of the cofactor matrix of A.
• Question 31
  • Solve the following system of equations: [x + 2y - z = 5] [2x - 3y + 4z = 10] [3x + 4y + 2z = 7]
• Question 32
  • Given matrix A as follows: A = [3 -2 1] [0 2 4] [-1 3 2]
  • Compute A^T, the transpose of matrix A.

Matrix and Determinant - Practice Questions

• Question 33
  • Calculate the determinant of the following matrix: [2 4 1 3] [5 6 2 5] [3 1 0 2] [1 2 3 4]
• Question 34
  • Solve the following system of equations: [2x + y - 3z = 1] [4x + 3y + z = 4] [3x - y + 2z = -1]
• Question 35
  • Given matrix A as follows: A = [1 2 -1] [0 3 4] [2 1 2]
  • Find the eigenvalues and eigenvectors of matrix A.

Matrix and Determinant - Practice Questions

• Question 36
  • Find the inverse of matrix A: A = [2 -3] [4 -5]
• Question 37
  • Solve the following system of equations: [x + y - z = 1] [2x + 2y + z = 3] [3x - y + 2z = 2]
• Question 38
  • Given matrix A as follows: A = [1 -1 2] [2 0 1] [-1 3 2]
  • Determine whether matrix A is orthogonal or not.

Matrix and Determinant - Practice Questions

• Question 39
  • Calculate the product of matrices A and B: A = [1 -2 -1] [2 3 1] [-1 1 0] B = [3 1 2] [2 -3 0] [1 0 4]
• Question 40
  • Solve the following system of equations: [2x + 3y - z = 4] [x - 2y + z = 1] [3x + y - 2z = 3]
• Question 41
  • Given matrix A as follows: A = [2 -1] [1 3]
  • Determine whether matrix A is a positive definite matrix.

Matrix and Determinant - Practice Questions

• Question 42
  • Find the eigenvalues and eigenvectors of matrix A: A = [3 4] [1 5]
• Question 43
  • Solve the following system of equations: [2x + 3y - z = 9] [4x - 2y + 5z = 15] [x + 2y + 3z = 7]
• Question 44
  • Given matrix A as follows: A = [1 -2 3] [4 -1 2] [2 3 -1]
  • Determine whether matrix A is diagonalizable or not.

Matrix and Determinant - Practice Questions

• Question 45
  • Calculate the determinant of the matrix A: A = [-1 2 3] [2 0 -1] [4 3 2]
• Question 46
  • Solve the following system of equations: [x + 2y + 3z = 2] [2x - y + 5z = 1] [3x + 4y - 2z = -3]
• Question 47
  • Given matrix A as follows: A = [2 -1 0] [4 2 -1] [6 3 1]
  • Determine whether matrix A is symmetric or not.

Matrix and Determinant - Practice Questions

• Question 48
  • Find the inverse of matrix A: A = [3 1] [4 2]
• Question 49
  • Solve the following system of equations: [3x + y - 2z = 5] [x - 2y + z = 2] [2x + 3y + z = 8]
• Question 50
  • Given matrix A as follows: A = [4 5 -1] [2 1 3] [1 2 -2]
  • Compute the adjoint of matrix A.

Matrix and Determinant - Practice Questions

• Question 51
  • Calculate the product of matrices A and B: A = [1 3 2] [4 2 -1] B = [2 1] [-3 2] [0 4]
• Question 52
  • Solve the following system of equations: [2x + 3y - z = 10] [x - 2y + z = 3] [3x + y + 2z = 5]
• Question 53
  • Given matrix A as follows: A = [2 -1 3] [1 1 2] [3 -2 4]
  • Determine whether matrix A is invertible or not.

Matrix and Determinant - Practice Questions

• Question 54
  • Find the eigenvalues and eigenvectors of matrix A: A = [2 -1] [3 4]
• Question 55
  • Solve the following system of equations: [x + y + z = 1] [2x - y - z = -2] [3x - y + 2z = 3]
• Question 56
  • Given matrix A as follows: A = [3 1 -2] [1 2 3] [2 3 1]
  • Determine whether matrix A is normal or not.

Matrix and Determinant - Practice Questions

• Question 57
  • Calculate the determinant of matrix A: A = [3 -2 1] [0 1 0] [4 -1 2]
• Question 58
  • Solve the following system of equations: [x + 2y + z = 3] [2x - 3y + 4z = 1] [3x + 4y - 2z = -2]
• Question 59
  • Given matrix A as follows: A = [1 2 -1] [0 2 3] [1 1 4]
  • Determine whether matrix A is orthogonal or not.