Lesson Worksheet: Inverse of a Matrix: Row Operations Mathematics

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

Q1:

Find the multiplicative inverse of the matrix 100710801.

  • A178010001
  • B100710801
  • C100710801
  • D178010001

Q2:

Find the multiplicative inverse of 1470010001.

  • A1004710001
  • B1004710001
  • C1470010001
  • D1470010001

Q3:

Use the inverse matrix to solve 3585123124721353𝑥𝑦𝑧𝑤=0101. Give your answer as an appropriate matrix.

  • A7822
  • B7822
  • C1.754.520.25
  • D71881
  • E2520

Q4:

Using elementary row operations, find 𝐴 for the matrix 𝐴=112303330 if possible.

  • A𝐴=13963643953
  • B𝐴=13963643953
  • CThe matrix has no inverse.
  • D𝐴=963643953
  • E𝐴=13963643953

Q5:

Using elementary row operations, find 𝐴, if possible, for the matrix 𝐴=011511233.

  • A𝐴=1460213251725
  • B𝐴=1460213251725
  • C𝐴=1460213251725
  • D𝐴=1460213251725
  • EThe matrix has no inverse.

Q6:

Using the elementary row operation, find 𝐴 for the matrix 𝐴=5321 if possible.

  • A𝐴=1325
  • B𝐴=1325
  • C𝐴=3152
  • D𝐴=1325
  • E𝐴=3152

Q7:

Consider 𝐴=1245. Find the inverse of the matrix 𝐴 using elementary row operations.

  • A1121415
  • B1121415
  • C53234313
  • D13234353
  • E53234313

Q8:

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

  • A0
  • B𝐼
  • C𝐴
  • D𝐴
  • E𝐴

Q9:

If 𝐼=𝐸𝐸𝐸𝐸𝐴, is 𝐴=𝐼𝐸𝐸𝐸𝐸 true?

  • AYes
  • BNo

Q10:

Using elementary row operations, find 𝐴, if possible, for the matrix 𝐴=3585123124721353.

  • A𝐴=2523321502101101
  • B𝐴=3215252302101101
  • CThe matrix has no inverse.
  • D𝐴=143215252302101101
  • E𝐴=1432152166208401211

This lesson includes 18 additional question variations for subscribers.

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