# Worksheet: Inverse of a Matrix: The Adjoint Method

In this worksheet, we will practice finding the inverse of 3x3 matrices using the adjoint method.

**Q3: **

Use technology to find the inverse of the matrix

- A
- B
- C
- D
- E

**Q4: **

Use technology to find the inverse of the matrix

- A
- B
- C
- D
- E

**Q5: **

Use technology to find the inverse of the matrix

- A
- B
- C
- D
- E

**Q6: **

Find the multiplicative inverse of the matrix

- A
- B
- C
- D

**Q7: **

Consider the matrix Find its inverse, given that it has the form , where , , and are numbers that you should find.

- A
- B
- C
- D
- E

**Q8: **

Consider the matrix Find its inverse, given that it has the form where , , , , , and are numbers you should find.

- A
- B
- C
- D
- E

**Q9: **

Consider the matrix Find its inverse, given that it has the form where , , and are expressions involving , , and that you should find.

- A
- B
- C
- D
- E

**Q10: **

Consider the matrix

Find its inverse, given that it has the form where , , , , , and are expressions involving , , , , , and that you should find.

- A (i.e., none of and is zero)
- B (i.e., neither nor is zero)
- C (i.e., none of and is zero)
- D (i.e., none of and is zero)
- E (i.e., none of and is zero)

**Q11: **

Using elementary row operations, find , if possible, for the matrix

- A
- B
- CThe matrix has no inverse.
- D
- E

**Q12: **

Find the cofactor matrix of

- A
- B
- C
- D

**Q13: **

Given that determine the value of .

**Q15: **

Determine whether the matrix has an inverse by finding whether the determinant is nonzero. If the determinant is nonzero, find the inverse using the inverse formula involving the cofactor matrix.

- AIt has an inverse, which is .
- BIt has an inverse, which is .
- CIt has an inverse, which is .
- DIt has an inverse, which is .
- EThe matrix has no inverse.

**Q16: **

Consider the matrix Determine whether the matrix has an inverse by finding whether the determinant is nonzero. If the determinant is nonzero, find the inverse using the formula for the inverse which involves the cofactor matrix.

- AThere is no inverse because its determinant equals zero.
- BIt has an inverse, which is .
- CIt has an inverse, which is .
- DIt has an inverse, which is .
- EIt has an inverse, which is .

**Q18: **

If is a square matrix and , what is ?

- A
- B
- C
- D

**Q20: **

Find the adjoint matrix of the matrix

- A
- B
- C
- D

**Q22: **

Find the value of that makes the matrix singular.

**Q24: **

Does the matrix have a multiplicative inverse?

- AYes
- BNo

**Q25: **

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

- A
- B
- C
- D