Matrix Algebra Quiz

Question 1: Perform the following matrix operations: A = [[2, 3], [4, 5]], B = [[1, 2], [3, 4]]. Find the sum of A and B.

• [[6, 8], [10, 12]]

• [[1, 2], [3, 4]]

• [[3, 5], [7, 9]]

• [[5, 7], [9, 11]]

Question 2: Perform the following matrix operations: A = [[2, 3], [4, 5]], B = [[1, 2], [3, 4]]. Find the product of A and B.

• [[11, 16], [19, 28]]

• [[3, 5], [7, 9]]

• [[8, 11], [12, 17]]

• [[5, 7], [9, 12]]

Question 3: Calculate the determinant of the matrix: A = [[3, 1], [2, 4]].

• 3

• 7

• 10

• 12

Question 4: Calculate the determinant of the matrix: A = [[5, 2, 1], [3, 6, 2], [4, 1, 3]].

• 7

• 10

• 18

• 25

Question 5: Find the eigenvalues of the matrix: A = [[4, 1], [2, 3]].

• The eigenvalues of the matrix A = [[4, 1], [2, 3]] are 1 and 4.

• The eigenvalues of the matrix A = [[4, 1], [2, 3]] are 7 and 2.

• The eigenvalues of the matrix A = [[4, 1], [2, 3]] are 6 and 3.

• The eigenvalues of the matrix A = [[4, 1], [2, 3]] are 5 and 2.

Question 6: Find the eigenvectors of the matrix: A = [[-2, 1], [1, -2]].

• [2, -1]

• The eigenvectors of the matrix A = [[-2, 1], [1, -2]] are [1, 1] and [-1, 1].

• [-1, -1]

• [0, 1]

Question 7: Solve the following system of linear equations: 2x + 3y = 8, 4x - 5y = -7.

• x = 3, y = 2

• x = 2, y = 4

• x = -1, y = 3

• x = 5, y = 1

Question 8: Solve the following system of linear equations: 3x + 2y - z = 7, 2x - y + 3z = 8, x + 3y - 2z = 9.

• x = 1, y = 4, z = 3

• x = 5, y = 1, z = 2

• x = 2, y = 3, z = 4

• x = 3, y = 2, z = 5

Question 9: Perform a 90-degree clockwise rotation on the matrix: A = [[1, 2], [3, 4]].

• [[4, 3], [2, 1]]

• [[3, 1], [4, 2]]

• [[2, 1], [4, 3]]

• [[1, 3], [2, 4]]

Question 10: Perform a horizontal shear transformation on the matrix: A = [[1, 2], [3, 4]].

• A = [[1, 2], [3, 4]] * S = [[1, 2], [3, 4]] * [[1, 1], [0, 1]] = [[1, 3], [3, 7]]

• A = [[1, 2], [3, 4]] * S = [[1, 2], [3, 4]] * [[1, 1], [1, 0]] = [[1, 3], [3, 7]]

• A = [[1, 2], [3, 4]] * S = [[1, 2], [3, 4]] * [[1, 0], [1, 1]] = [[1, 3], [3, 7]]

• A = [[1, 2], [3, 4]] * S = [[1, 2], [3, 4]] * [[1, 0], [0, 1]] = [[1, 2], [3, 4]]