# Worksheet: Inverse of a Matrix: Row Operations

In this worksheet, we will practice using elementary row operations to find the inverse of a matrix, if possible.

Q1:

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

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

Q2:

Find the multiplicative inverse of

• A
• B
• C
• D

Q3:

Use the inverse matrix to solve Give your answer as an appropriate matrix.

• A
• B
• C
• D
• E

Q4:

Find , given that

• A
• B
• C
• D
• E

Q5:

Find the multiplicative inverse of the matrix

• A
• B
• C
• D

Q6:

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

• A
• B
• C
• D
• E

Q7:

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

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

Q8:

Solve this system of equations using the inverse matrix

Give your solution as an appropriate matrix whose elements are expressed in terms of , , , and .

• A
• B
• C
• D
• E

Q9:

Consider . Find the inverse of the matrix using elementary row operations.

• A
• B
• C
• D
• E

Q10:

If a set of row operations () are performed on a matrix until it is transformed into the identity matrix, what is the matrix resulting from performing the same row operations on the identity matrix?

• A0
• B
• C
• D
• E

Q11:

If , is true?

• AYes
• BNo