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Worksheet: Finding the Inverse of 3 x 3 Matrix
Q1:
By considering the value of the determinant, determine whether the matrix has an inverse. If so, find the inverse by considering the matrix of cofactors.
- AIt has an inverse, .
- BIt has an inverse, .
- CIt has an inverse, .
- DIt has an inverse, .
- EIt has no inverse.
Q2:
Find the inverse of the following matrix.
- A
- B
- C
- D
- E
Q3:
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 .
- E The matrix has no inverse.
Q4:
Find, if it exists, the inverse of the matrix
- A
- B
- C
- D
- E
Q5:
Use technology to find the inverse of the following matrix.
- A
- B
- C
- D
- E
Q6:
Use technology to find the inverse of the following matrix.
- A
- B
- C
- D
- E
Q7:
Use technology to find the inverse of the following matrix.
- A
- B
- C
- D
- E
Q8:
Using the elementary row operation, find for the given matrix if possible.
- A
- B
- C
- D
- E The matrix has no inverse.
Q9:
Using the Cayley-Hamilton theorem, find for the given matrix if possible.
- A
- B
- C
- D
- EThe matrix has no inverse.
Q10:
Using elementary row operations, find for the given matrix if possible.
- A
- B
- C
- D The matrix has no inverse.
- E
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