Matrix Inversion Using Row Operations Quiz

What is the purpose of adding an identity matrix to the right side of the augmented matrix?

• To help find the inverse of the original matrix

• To make calculations easier

• To check the consistency of the matrix

• To simplify the matrix

Which of the following is NOT an elementary row operation?

• Multiplying a row by a nonzero constant

• Adding one row to another

• Interchanging two rows

• Dividing a row by zero

Why is it important to follow a specific order when achieving zeros in the matrix?

• To avoid making the matrix singular

• To prevent undoing previous steps

• To ensure the matrix remains square

• To make the matrix symmetric

What is the result of multiplying Row 2 by -1 and adding it to Row 3?

• 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

How can you achieve a zero in the third position of the matrix?

• 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

What is the lowest common multiple used to achieve a zero in the fourth position?

• 15

• 6

• 12

• 9

What operation is performed to achieve a zero in the fifth position?

• 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

What is the final step to ensure the matrix on the left is the identity matrix?

• 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

How can you verify that the matrix on the right is the inverse of the original matrix?

• 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

What should you do if you want to practice more on matrices?

• Solve problems on determinants

• Watch more videos on elementary row operations

• Study eigenvalues and eigenvectors

• Read a book on linear algebra