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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