# Worksheet: Transpose of a Matrix

In this worksheet, we will practice finding the transpose of a matrix and identifying symmetric and skew-symmetric matrices.

Q1:

Find the transpose of the matrix .

• A
• B
• C
• D

Q2:

Given the matrix find .

• A
• B
• C
• D

Q3:

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

• A
• B
• C
• D

Q4:

Given the matrices , , does ?

• ANo
• BYes

Q5:

Find the transpose of the matrix .

• A
• B
• C
• D

Q6:

Find the transpose of the matrix .

• A
• B
• C
• D

Q7:

Find the transpose of the matrix .

• A
• B
• C
• D

Q8:

Which of the following matrices is skew-symmetric?

• A
• B
• C
• D

Q9:

Given that the matrix is skew-symmetric, find the value of .

Q10:

Find the value of which makes the matrix symmetric.

Q11:

If is a symmetric matrix, what are the values of , , and ?

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q12:

Which of the following matrices is symmetric?

• A
• B
• C
• D

Q13:

Given that where , find the matrix . That is matrix.

• A
• B
• C
• D

Q14:

Consider the matrices , . Determine and .

• A,
• B,
• C,
• D,
• E,

Q15:

Given that find .

• A
• B
• C
• D

Q16:

Given that determine the matrix .

• A
• B
• C
• D

Q17:

Given that find the result of , if possible.

• A
• BIt is not possible.
• C
• D
• E

Q18:

Find .

• A
• B
• Cnot possible
• D
• E

Q19:

Given that is a zero matrix, find .

• A
• B
• C
• D
• E

Q20:

If is a skew-symmetric matrix, then .

• A
• B
• C
• D

Q21:

If is a symmetric matrix, then which of the following can be a rule to deduce the element of matrix ?

• A
• B
• C
• D

Q22:

If , then .

• A
• B
• C
• D

Q23:

If and are two symmetric matrices, then matrix is .

• Asymmetric
• Btriangular
• Cskew symmetric
• Ddiagonal

Q24:

If is skew symmetric, then .

• A1
• B
• C0
• D

Q25:

If is a square matrix and , then is a matrix.