# Worksheet: Transpose of a Matrix

Q1:

What operation must be performed on the matrix to get the matrix ? How does this operation affect the value of the determinant?

• AThe second matrix is the first matrix with the columns swapped. The determinant of the second matrix is times the determinant of the first matrix.
• BThe second matrix is the inverse of the first. The determinant of the second matrix is the reciprocal of the determinant of the first matrix.
• CThe second matrix is the first matrix with the rows swapped. The determinant of the second matrix is times the determinant of the first matrix.
• DThe second matrix is the transpose of the first. The determinant of the second matrix is the same as the determinant of the first matrix.
• EThe second matrix is the inverse of the first. The determinant of the second matrix is the same as the determinant of the first matrix.

Q2:

Consider the given matrices. Is it true that ?

• Ayes
• Bno

Q3:

If is a matrix of order , then what is the order of the matrix ?

• A
• B
• C
• D

Q4:

If and , what is ?

• A
• B
• C
• D

Q5:

Given that what is ?

• A
• B
• C
• D

Q6:

Given that determine the value of .

• A20
• B8
• C
• D0

Q7:

Find the transpose of the matrix .

• A
• B
• C
• D

Q8:

Find the transpose of the matrix .

• A
• B
• C
• D

Q9:

Find the transpose of the matrix .

• A
• B
• C
• D

Q10:

Find the transpose of the matrix .

• A
• B
• C
• D

Q11:

Give the following matrix, find .

• A
• B
• C
• D

Q12:

Given the shown matrices, determine whether .

• Ayes
• Bno