# Worksheet: Orthogonal Matrices

In this worksheet, we will practice determining whether a matrix is orthogonal and finding its inverse if it is.

Q1:

Is the matrix orthogonal?

• ANo
• BYes

Q2:

Is the given matrix orthogonal?

• AYes
• BNo

Q3:

Is the matrix orthogonal?

• ANo
• BYes

Q4:

Is the matrix orthogonal?

• AYes
• BNo

Q5:

Given that the matrix is orthogonal, find the values of , , , and .

• A, , ,
• B, , ,
• C, , ,
• D, , ,
• E, , ,

Q6:

Given that the matrix is orthogonal, find the values of , , , and .

• A, , ,
• B, , ,
• C, , ,
• D, , ,
• E, , ,

Q7:

Given that the matrix is orthogonal, find the values of , , , and .

• A, , ,
• B, , ,
• C, , ,
• D, , ,
• E, , ,

Q8:

Fill in the missing entries to make the matrix orthogonal.

• A
• B
• C
• D
• E

Q9:

A matrix is said to be orthogonal if . Thus, the inverse of an orthogonal matrix is just its transpose. What are the possible values of if is an orthogonal matrix?

• A or
• B
• C or
• D or
• E

Q10:

True or false: the matrix is orthogonal?

• AFalse
• BTrue

Q11:

If is an orthogonal matrix, which of the following may not be true about ?

• A.
• BThe rows of form an orthonormal basis for .
• CThe determinant of equals 1.
• DThe columns of form an orthonormal basis for .
• EThe nullity of is 0.

Q12:

Determine whether the following matrix is orthogonal:

• A is an orthogonal matrix.
• B is not an orthogonal matrix.

Q13:

Determine whether the following matrix is orthogonal:

• AThe matrix is orthogonal.
• BThe matrix is not orthogonal.