Worksheet: Inverse of a 3x3 Matrix

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In this worksheet, we will practice finding the inverse matrix for a given three-by-three 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:

Use technology to find the inverse of the following matrix.

  • A
  • B
  • C
  • D
  • E

Q4:

Use technology to find the inverse of the following matrix.

  • A
  • B
  • C
  • D
  • E

Q5:

Use technology to find the inverse of the following matrix.

  • A
  • B
  • C
  • D
  • E

Q6:

Using the elementary row operation, find for the given matrix if possible.

  • A
  • B
  • C
  • D
  • E The matrix has no inverse.

Q7:

Using the Cayley-Hamilton theorem, find for the given matrix if possible.

  • A
  • B
  • C
  • D
  • EThe matrix has no inverse.

Q8:

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

  • A
  • B
  • C
  • D The matrix has no inverse.
  • E

Q9:

Find the multiplicative inverse of

  • A 1 4 7 0 0 1 0 0 0 1
  • B 1 0 0 − 4 7 1 0 0 0 1
  • C 1 0 0 4 7 1 0 0 0 1
  • D 1 − 4 7 0 0 1 0 0 0 1

Q10:

Find the multiplicative inverse of the matrix

  • A 1 7 8 0 1 0 0 0 1
  • B 1 0 0 7 1 0 8 0 1
  • C 1 − 7 − 8 0 1 0 0 0 1
  • D 1 0 0 − 7 1 0 − 8 0 1

Q11:

Find the multiplicative inverse of the matrix

  • A − 1 1 2 5 − 2 5 0 0 0 − 2 5 0 0 0 − 2 5
  • B 2 5 0 0 0 2 5 0 0 0 2 5
  • C − 2 5 0 0 0 − 2 5 0 0 0 − 2 5
  • D − 1 1 2 5 2 5 0 0 0 2 5 0 0 0 2 5

Q12:

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

Q13:

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

  • A
  • B
  • C
  • D