Quiz-4 Linear Algebra

Which of the following is the correct definition of a vector in linear algebra?

• A scalar quantity

• A quantity with magnitude and direction

• A quantity with magnitude only

• A matrix with a single row or column

What is the determinant of a 2x2 matrix with elements a, b, c, and d?

• ad - bc

• ac - bd

• ad + bc

• bc - ad

Given two matrices A and B, under what condition can you perform matrix multiplication A * B?

• The number of columns in A is equal to the number of rows in B

• The number of rows in A is equal to the number of columns in B

• The number of rows in A is equal to the number of rows in B

• The number of columns in A is equal to the number of columns in B

Which of the following operations is NOT a valid elementary row operation in matrix manipulation?

• Interchanging two rows

• Multiplying a row by a non-zero constant

• Adding a multiple of one row to another row

• Dividing a row by a non-zero constant

If a square matrix A is multiplied by its inverse, the result is:

• The identity matrix

• The zero matrix

• A matrix with all elements equal to one

• A matrix with all elements equal to zero

The eigenvalues of a matrix are the solutions to:

• Ax = 0

• Ax = b

• |A| = 0

• |A| = λI

Which of the following statements about eigenvectors is true?

• Eigenvectors always have distinct eigenvalues

• Eigenvectors are always perpendicular to each other

• A matrix can have multiple linearly independent eigenvectors corresponding to the same eigenvalue

• Eigenvectors are always the columns of the identity matrix

The rank of a matrix is defined as:

• The sum of all its elements

• The number of rows in the matrix

• The number of columns in the matrix

• The maximum number of linearly independent rows or columns

What is the mean of the following data set: [02, 05, 08, 11, 14]?

The median of the data set [05, 08, 12, 15, 18] is