Linear Algebra Mastery

Find the sum of the matrices A = [1 2; 3 4] and B = [5 6; 7 8].

• [2 4; 6 8]

• [7 9; 11 13]

• [6 8; 10 12]

• [10 12; 14 16]

Calculate the product of the matrices C = [2 3; 4 5] and D = [1 2; 3 4].

• [3 5; 7 9]

• [5 8; 9 12]

• [8 14; 14 24]

• [10 15; 15 20]

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

• x = 3, y = 2

• x = 2, y = 1

• x = 5, y = 4

• x = 1, y = 3

Find the Eigenvalues of the matrix E = [3 1; 2 4].

• The eigenvalues of the matrix E = [3 1; 2 4] are λ1 = 2 and λ2 = 5.

• λ1 = 0 and λ2 = 7

• λ1 = 1 and λ2 = 6

• λ1 = 3 and λ2 = 4

Calculate the Eigenvectors corresponding to the Eigenvalue λ = 5 for the matrix F = [2 1; 1 3].

• The Eigenvectors corresponding to the Eigenvalue λ = 5 for the matrix F = [2 1; 1 3] are [0; 0]

• The Eigenvectors corresponding to the Eigenvalue λ = 5 for the matrix F = [2 1; 1 3] are [2; 3]

• The Eigenvectors corresponding to the Eigenvalue λ = 5 for the matrix F = [2 1; 1 3] are [3; 2]

• The Eigenvectors corresponding to the Eigenvalue λ = 5 for the matrix F = [2 1; 1 3] are [1; 1]

Diagonalize the matrix G = [4 1; 2 3].

• The matrix G = [4 1; 2 3] can be diagonalized by finding its eigenvalues and eigenvectors.

• The matrix G = [4 1; 2 3] can be diagonalized by multiplying it with its inverse.

• The matrix G = [4 1; 2 3] cannot be diagonalized.

• The matrix G = [4 1; 2 3] can be diagonalized by transposing it.

What are the applications of linear algebra in computer graphics?

• Creating spreadsheets

• Developing mobile apps

• Building websites

• 3D transformations, rendering, and image processing

Explain the role of linear algebra in machine learning.

• It is only relevant for advanced statistical analysis

• Linear algebra has no role in machine learning

• It is only used for basic arithmetic operations

• It is essential for tasks such as solving systems of linear equations, dimensionality reduction, and working with matrices and vectors.

How is linear algebra used in cryptography?

• Linear algebra is used for designing secure physical locks

• Linear algebra is used for encryption, decryption, and key generation.

• Linear algebra is used for creating new cryptographic algorithms

• Linear algebra is used for analyzing historical ciphers

What are the practical applications of matrix algebra in real life?

• Matrix algebra has practical applications in various fields such as computer graphics, cryptography, economics, engineering, and physics.

• Matrix algebra is only used in space travel

• Matrix algebra is only used in cooking recipes

• Matrix algebra is only used in ancient history