Mastering Matrix Concepts

Perform the operation: A = [[1, 2], [3, 4]], B = [[5, 6], [7, 8]]. What is A + B?

• [[8, 10], [12, 14]]

• [[1, 2, 3], [4, 5, 6]]

• [[5, 6], [7, 8]]

• [[6, 8], [10, 12]]

Calculate the determinant of the matrix: [[2, 3], [5, 7]].

• 0

• 10

• -5

• -1

Find the inverse of the matrix: [[4, 7], [2, 6]].

• [[4, 5], [6, 7]]

• [[0.6, -0.7], [-0.2, 0.4]]

• [[1, 0], [0, 1]]

• [[2, 3], [1, 2]]

Determine the eigenvalues of the matrix: [[1, 2], [3, 4]].

• (3 ± √5) / 2

• (5 ± √29) / 2

• (6 ± √10) / 2

• (4 ± √20) / 2

Find the eigenvectors corresponding to the eigenvalue 5 of the matrix: [[1, 2], [3, 4]].

• Any non-zero scalar multiple of [1, 2]

• [3, 1]

• [0, 0]

• [2, 1]

Describe the transformation represented by the matrix: [[0, -1], [1, 0]].

• 180-degree rotation

• 90-degree counterclockwise rotation

• 90-degree clockwise rotation

• No transformation

Solve the system of equations: 2x + 3y = 6, 4x - y = 5.

• x = 1, y = 2

• x = 0, y = 2

• x = 2, y = 0

• x = 3/2, y = 1

What is the application of matrices in computer graphics?

• Matrices are used for color blending in computer graphics.

• Matrices are primarily for storing pixel data in images.

• Matrices are used to create sound effects in animations.

• Matrices are used for transformations (translation, rotation, scaling) in computer graphics.

If A = [[1, 2], [3, 4]] and B = [[5], [6]], what is the product AB?

• [[20], [30]]

• [[17], [39]]

• [[15], [35]]

• [[10], [24]]

Explain how matrices can be used to represent networks.

• Matrices can only represent numerical data.

• Networks cannot be represented using mathematical concepts.

• Matrices are exclusively used for image processing.

• Matrices can represent networks through adjacency and incidence matrices.