Matrix Inversion Using Row Operations Quiz

To help find the inverse of the original matrix

To make calculations easier

To check the consistency of the matrix

To simplify the matrix

Multiplying a row by a nonzero constant

Adding one row to another

Interchanging two rows

Dividing a row by zero

To avoid making the matrix singular

To prevent undoing previous steps

To ensure the matrix remains square

To make the matrix symmetric

A new row with a zero in the first position

A new row with a zero in the third position

A new row with a zero in the second position

A new row with all zeros

By adding Row 1 to Row 2

By subtracting Row 3 from Row 2

By adding Row 2 to Row 3

By multiplying Row 1 by 2

15

6

12

9

Multiplying Row 1 by 3 and adding to Row 3

Multiplying Row 2 by 2 and adding to Row 1

Multiplying Row 3 by 3 and adding to Row 1

Multiplying Row 1 by 2 and adding to Row 2

Multiply each row by its reciprocal

Subtract the first row from the last row

Multiply each row by a constant to get ones on the diagonal

Add all rows together

By subtracting it from the original matrix

By checking if the determinant is zero

By multiplying it with the original matrix to get the identity matrix

By adding it to the original matrix

Solve problems on determinants

Watch more videos on elementary row operations

Study eigenvalues and eigenvectors

Read a book on linear algebra