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Row & Column Operations: Matrices and Determinants Video Lecture | Business Mathematics and Statistics - B Com
FAQs on Row & Column Operations: Matrices and Determinants Video Lecture - Business Mathematics and Statistics - B Com
| 1. What are row operations in matrices? |  |
Ans.Row operations are techniques used to manipulate the rows of a matrix to simplify it or to solve systems of linear equations. There are three types of row operations:
1. Swapping two rows.
2. Multiplying a row by a non-zero scalar.
3. Adding or subtracting a multiple of one row to another row.
| 2. How do column operations differ from row operations? | |
Ans.Column operations are similar to row operations but applied to the columns of a matrix. The types of column operations include:
1. Swapping two columns.
2. Multiplying a column by a non-zero scalar.
3. Adding or subtracting a multiple of one column to another column. These operations are useful in transforming matrices to find determinants or solve linear equations.
| 3. What is the significance of row echelon form in solving linear equations? | |
Ans.Row echelon form (REF) is significant because it simplifies the process of solving a system of linear equations. A matrix is in REF if all non-zero rows are above any rows of zeros, and the leading coefficient of a non-zero row is always to the right of the leading coefficient of the previous row. This form allows for easier back substitution to find the solutions of the equations.
| 4. How do determinant properties relate to row and column operations? | |
Ans.Determinants have specific properties that relate to row and column operations. For example, swapping two rows or columns changes the sign of the determinant. Multiplying a row or column by a scalar multiplies the determinant by that scalar. Adding a multiple of one row or column to another does not change the determinant. Understanding these properties is crucial for calculating determinants efficiently.
| 5. What is the relationship between the rank of a matrix and row operations? | |
Ans.The rank of a matrix is defined as the maximum number of linearly independent row or column vectors in the matrix. Row operations do not change the rank of a matrix; they simply alter its form. By transforming a matrix using row operations to its row echelon form or reduced row echelon form, one can easily determine its rank by counting the number of non-zero rows.
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