Understanding Matrices

What is the sum of the matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]?

• [[6, 10], [12, 14]]

• [[1, 2], [3, 4]]

• [[5, 6], [7, 8]]

• [[6, 8], [10, 12]]

Calculate the determinant of the matrix C = [[2, 3], [1, 4]].

• 8

• 7

• 6

• 5

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

• [[1, 0], [0, 1]]

• [[2, 3], [1, 2]]

• [[0.6, -0.7], [-0.2, 0.4]]

• [[5, 1], [3, 4]]

What is the order of the matrix E = [[1, 2, 3], [4, 5, 6]]?

• 1x3

• 3x2

• 2x3

• 2x2

Explain one real-world application of matrices.

• In organizing data in spreadsheets for calculations.

• In computer graphics for transformations of images.

• In creating music compositions using sound frequencies.

• In solving linear equations for physics problems.

If F = [[1, 0], [0, 1]] is an identity matrix, what is F multiplied by any matrix G?

• F

• 0

• G

• G multiplied by itself

What is the result of adding the matrices H = [[2, 3], [4, 5]] and I = [[1, 1], [1, 1]]?

• [[1, 2], [3, 4]]

• [[2, 3], [4, 5]]

• [[3, 4], [5, 6]]

• [[0, 0], [0, 0]]

Determine the determinant of the matrix J = [[3, 2], [1, 4]].

• 10

• 12

• 8

• 5

What is the inverse of the matrix K = [[1, 2], [3, 4]]?

• [[1, 0], [0, 1]]

• [[0.5, -1], [-1.5, 2]]

• [[-2.0, 1.0], [1.5, -0.5]]

• [[4, 3], [2, 1]]

What is the order of the matrix L = [[1], [2], [3]]?

• 3x1

• 1x3

• 4x1

• 2x2