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Elementary Operations (Transformation) of a Matrix Video Lecture | Mathematics (Maths) Class 12 - JEE

204 videos|288 docs|139 tests

FAQs on Elementary Operations (Transformation) of a Matrix Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What are elementary operations of a matrix?
Ans. Elementary operations of a matrix refer to the three basic operations that can be performed on its rows or columns. These operations include swapping two rows or columns, multiplying a row or column by a nonzero scalar, and adding a multiple of one row or column to another row or column.
2. How are elementary operations useful in matrix operations?
Ans. Elementary operations are useful in matrix operations as they allow us to manipulate the matrix in a systematic way. By performing these operations, we can simplify the matrix, solve systems of linear equations, find the inverse of a matrix, and determine properties such as rank and determinant.
3. Can elementary operations change the solutions of a system of equations represented by a matrix?
Ans. No, elementary operations do not change the solutions of a system of equations represented by a matrix. The solutions remain the same even after performing elementary operations on the matrix. However, these operations can help us in finding the solutions by transforming the matrix into a simpler form.
4. Is it possible to transform a matrix into its row-echelon form using elementary operations?
Ans. Yes, it is possible to transform a matrix into its row-echelon form using elementary operations. By applying a sequence of row operations, we can eliminate all entries below the main diagonal of the matrix, resulting in a row-echelon form. This form is useful for solving systems of linear equations and finding the rank of the matrix.
5. Can elementary operations be applied to non-square matrices?
Ans. Yes, elementary operations can be applied to non-square matrices as well. These operations can be performed on both rows and columns of the matrix, regardless of its dimensions. By using elementary operations, we can simplify the matrix, find its rank, and perform other operations similar to those on square matrices.
204 videos|288 docs|139 tests

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