Linear Algebra Using Python

What is the definition of a vector in linear algebra?

• A type of insect

• A mathematical object that has both magnitude and direction, represented as an array of numbers.

• A form of transportation

• A type of musical instrument

Explain the concept of matrix multiplication with an example in Python.

• Matrix multiplication in Python is performed using the '+' operator

• Matrix multiplication is not supported in Python

• Matrix multiplication is performed using the '@' operator in Python. For example, if A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then A @ B will result in [[19, 22], [43, 50]].

• Matrix multiplication in Python is performed using the '-' operator

Write a Python function to calculate the dot product of two vectors.

• def dot_product(vector1, vector2): return vector1 * vector2

• def dot_product(vector1, vector2): return sum(vector1 * vector2)

• def dot_product(vector1, vector2): return sum(vector1 + vector2)

• def dot_product(vector1, vector2): return sum(x * y for x, y in zip(vector1, vector2))

How can you find the determinant of a matrix using Python?

• import numpy as np; matrix = np.array([[1, 2], [3, 4]]); determinant = np.matrix.det(matrix)

• import numpy as np; matrix = np.array([[1, 2], [3, 4]]); determinant = np.linalg.det(matrix)

• import numpy as np; matrix = np.array([[1, 2], [3, 4]]); determinant = np.linalg.det(matrix)

• import numpy as np; matrix = np.array([[1, 2], [3, 4]]); determinant = np.linalg.determinant(matrix)

Write a Python code to find the inverse of a matrix.

• import numpy matrix = numpy.array([[1, 2], [3, 4]]) inverse_matrix = numpy.linalg.inv(matrix)

• matrix = numpy.array([[2, 3], [4, 5]])

• inverse_matrix = numpy.linalg.inverse(matrix)

• import pandas

What is the difference between a row vector and a column vector?

• A row vector is a 2xN matrix, while a column vector is a Nx2 matrix.

• A row vector is always a square matrix, while a column vector is always a rectangular matrix.

• A row vector is used for vertical operations, while a column vector is used for horizontal operations.

• A row vector is a 1xN matrix, while a column vector is a Nx1 matrix.

Explain the concept of span of vectors in linear algebra.

• The set of all possible linear combinations of those vectors.

• The difference of the vectors

• The product of the vectors

• The sum of the vectors

Write a Python function to perform matrix addition.

• def add_matrix(matrix1, matrix2):

• def matrix_addition(matrix1, matrix2): result = [] for i in range(len(matrix1)): row = [] for j in range(len(matrix1[0])): row.append(matrix1[i][j] + matrix2[i][j]) result.append(row) return result

• def multiply_matrix(matrix1, matrix2):

• def matrix_subtraction(matrix1, matrix2):

How can you use Python to solve a system of linear equations?

• TensorFlow library

• Pandas library

• Matplotlib library

• NumPy library

What is a correct syntax to create a NumPy array?

• np.createArray([1,2,3,4,5])

• np.array([1,2,3,4,5])

• np.object([1,2,3,4,5])

• np.Array([1,2,3,4,5])