# Worksheet: Invertible and Singular Matrices

In this worksheet, we will practice differentiating between invertible and singular matrices.

Q1:

Is the following matrix invertible?

• Ano
• Byes

Q2:

Under what condition on is the following matrix invertible?

• A is any real number
• B or
• C and
• D and
• E or

Q3:

Is there any value of for which the matrix has no inverse?

• Ayes, when
• Byes, when
• Cyes, when
• Dno
• Eyes, when

Q4:

Is there any value of for which the matrix has no inverse?

• Ayes, when
• Byes, when
• Cno
• Dyes, the matrix has no inverse for all values of
• Eyes, when

Q5:

Is there any value of for which the matrix has no inverse?

• A yes, when
• B yes, when
• C yes, when
• D no
• E yes, when

Q6:

Which of the following matrices is singular?

• A
• B
• C
• D

Q7:

Under what condition on and is the following matrix invertible?

• A
• B
• C
• D
• E

Q8:

Find the value of that makes the matrix singular.

• A
• B40
• C
• D

Q9:

Find all the values of for which the matrix is singular.

• A4
• B
• C196
• D

Q10:

Find the value of that makes the matrix singular.

Q11:

Find all the values of , where , which make the following matrix singular:

• A ,
• B ,
• C ,
• D ,

Q12:

Find the set of real values of for which has a multiplicative inverse.

• A
• B
• C
• D
• E

Q13:

For the matrix does there exist a value of for which it fails to have an inverse? if so, what is this value?

• A yes, when .
• B yes, when .
• C yes, when .
• D yes, when .
• E yes, when .

Q14:

Find the set of real values of for which has no multiplicative inverse.

• A
• B
• C
• D
• E

Q15:

Find the set of real values of for which has no multiplicative inverse.

• A
• B
• C
• D

Q16:

Find the set of real values of for which the following matrix has a multiplicative inverse

• A
• B
• C
• D
• E

Q17:

Find the set of real values of for which has a multiplicative inverse, where .

• A
• B
• C
• D

Q18:

Does the matrix have a multiplicative inverse?

• ANo
• BYes

Q19:

Find the set of real values of that make the following matrix singular.

• A
• B
• C
• D

Q20:

Find the set of real values of that make the matrix singular.

• A
• B
• C
• D

Q21:

Suppose is matrix in and is a vector in and consider this statement: there exists a solution to the equation . Which of the following is true?

• AThe statement is true if and only if is nonsingular.
• B If the statement is true, then is nonsingular.
• CThe statement is always true.
• DIf is nonsingular, then the statement is true.
• E If is nonsingular, then the statement is false.

Q22:

Which of the following matrices is singular?

• A
• B
• C
• D

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