Elementary Row Operations in Matrices

The video tutorial covers elementary row operations on matrices, including multiplying rows by a scalar, interchanging rows, and adding multiples of one row to another. It explains how to perform these operations step-by-step with examples, highlighting common scenarios students might encounter in homework. The tutorial also addresses how to handle row operations that are not attached to a specific row, providing guidance on where to place the results.

What is the result of multiplying each element of a row by a scalar?

• The row remains unchanged.

• Each element in the row is divided by the scalar.

• Each element in the row is multiplied by the scalar.

• The row is removed from the matrix.

What happens when you interchange two rows in a matrix?

• The two rows are added together.

• The matrix is transposed.

• The two rows swap their positions.

• The matrix becomes singular.

In a row operation where a multiple of one row is added to another, where are the results placed?

• In the last row of the matrix.

• In the first row.

• In the row specified by the operation.

• In a new row added to the matrix.

What is the result of the operation 2R1 + R3 if R1 is [3, 4, -2, 1] and R3 is [4, -3, 0, 2]?

• [3, 4, -2, 1]

• [6, 8, -4, 2]

• [7, 1, -2, 3]

• [10, 5, -4, 4]

If a row operation is not attached to a specific row, where should the results be placed?

• In the row mentioned last in the operation.

• In the row with the smallest index.

• In the row with the largest index.

• In the first row.

What is the result of adding 3 times the first row to the second row, if the first row is [4, 6, -2, 7] and the second row is [0, -8, 1, 3]?

• [12, 10, -5, 24]

• [4, -2, -1, 10]

• [12, 18, -6, 21]

• [0, -8, 1, 3]

What is the primary purpose of performing elementary row operations on a matrix?

• To increase the determinant of the matrix.

• To make the matrix symmetric.

• To solve systems of linear equations.

• To change the size of the matrix.

Which of the following is NOT an elementary row operation?

• Adding a multiple of one row to another row.

• Transposing the matrix.

• Interchanging two rows.

• Multiplying a row by a non-zero scalar.

What is the effect of multiplying a row by zero?

• The row is removed from the matrix.

• The row is multiplied by one.

• The row becomes a zero row.

• The row is unchanged.

Which operation would you use to make two rows identical?

• Add a multiple of one row to another.

• Multiply both rows by the same scalar.

• Multiply one row by zero.

• Interchange the two rows.