Worksheet: Finding the Inverse of a Three by Three Matrix

A matrix has an inverse if and only if its determinant is not equal to zero and the matrix itself is a square matrix. 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 no inverse.
BIt has an inverse, .
CIt has an inverse, .
DIt has an inverse, .
EIt has an inverse, .

Q2:

Find the inverse of the following matrix.

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.

AThe matrix has no inverse.
BIt has an inverse, which is .
CIt has an inverse, which is .
DIt has an inverse, which is .
EIt has an inverse, which is .

Q4:

Find, if it exists, the inverse of the matrix

Q5:

Use technology to find the inverse of the following matrix.

Q6:

Use technology to find the inverse of the following matrix.

Q7:

Use technology to find the inverse of the following matrix.

Q8:

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

AThe matrix has no inverse.
B
C
D
E

Q9:

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

AThe matrix has no inverse.
B
C
D
E

Q10:

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

A
B
CThe matrix has no inverse.
D
E