# 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