Matrix Types and Properties

This video tutorial covers various types of matrices, including row, column, null, square, identity, opposite, transposed, and symmetric matrices. It explains the characteristics and properties of each type, providing examples and highlighting key features such as diagonals in square matrices and the transformation of rows to columns in transposed matrices. The tutorial also discusses the concept of symmetric matrices, where the matrix is equal to its transposed form.

What is a row matrix?

• A matrix with all elements as zero

• A matrix with only one column

• A matrix with only one row

• A matrix with equal number of rows and columns

Which of the following is true about a column matrix?

• It has multiple rows and columns

• It has only one row

• It has only one column

• It has equal number of rows and columns

What is a null matrix?

• A matrix with equal number of rows and columns

• A matrix with only one column

• A matrix with only one row

• A matrix with all elements as zero

What defines a square matrix?

• It has equal number of rows and columns

• It has only one column

• It has only one row

• It has all elements as zero

In a square matrix, what is the diagonal that goes from the top left to the bottom right called?

• Secondary diagonal

• Main diagonal

• Horizontal diagonal

• Vertical diagonal

What is the main characteristic of an identity matrix?

• All elements are one

• All elements are zero

• Diagonal elements are one, and others are zero

• It has equal number of rows and columns

Which matrix type has all its diagonal elements as one and the rest as zero?

• Identity matrix

• Symmetric matrix

• Opposite matrix

• Null matrix

How is an opposite matrix obtained?

• By changing the sign of all elements

• By multiplying all elements by zero

• By subtracting one from all elements

• By adding one to all elements

What does the transposition of a matrix involve?

• Changing all elements to zero

• Changing rows into columns and columns into rows

• Multiplying all elements by one

• Changing the sign of all elements

What is a symmetric matrix?

• A matrix with only one column

• A matrix with only one row

• A matrix with all elements as zero

• A matrix that is equal to its transpose