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If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be ______ of A
- a)Equivalent
- b)Inverse
- c)Adjoint
- d)none of the above
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If a matrix B is obtained from matrix A by an elementary row or column...
ANSWER :- a
Solution :- Matrix equivalence is an equivalence relation on the space of rectangular matrices.
For two rectangular matrices of the same size, their equivalence can also be characterized by the following conditions
- The matrices can be transformed into one another by a combination of elementary row and column operations.
If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be equivalent of A.
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If a matrix B is obtained from matrix A by an elementary row or column...
Explanation:
When we perform an elementary row or column transformation on a matrix A, we get a new matrix B. These transformations include operations like multiplying a row or column by a non-zero scalar, interchanging two rows or columns, or adding a multiple of one row or column to another.
The resulting matrix B is said to be equivalent to A because it has the same row space, column space, rank, determinant, and other properties as A. This means that B can be transformed back into A using a sequence of elementary row or column operations.
For example, if we multiply a row of A by a non-zero scalar k, then the corresponding row of B will be k times the corresponding row of A. Similarly, if we add a multiple of one row to another row in A, then the corresponding rows in B will have the same relationship. These operations preserve the row space and rank of A, so B will have the same properties.
Therefore, we can say that B is equivalent to A because it can be transformed back into A using elementary row or column operations. This is an important concept in linear algebra because it allows us to simplify matrices and solve systems of linear equations by reducing them to their row echelon form.
When we perform an elementary row or column transformation on a matrix A, we get a new matrix B. These transformations include operations like multiplying a row or column by a non-zero scalar, interchanging two rows or columns, or adding a multiple of one row or column to another.
The resulting matrix B is said to be equivalent to A because it has the same row space, column space, rank, determinant, and other properties as A. This means that B can be transformed back into A using a sequence of elementary row or column operations.
For example, if we multiply a row of A by a non-zero scalar k, then the corresponding row of B will be k times the corresponding row of A. Similarly, if we add a multiple of one row to another row in A, then the corresponding rows in B will have the same relationship. These operations preserve the row space and rank of A, so B will have the same properties.
Therefore, we can say that B is equivalent to A because it can be transformed back into A using elementary row or column operations. This is an important concept in linear algebra because it allows us to simplify matrices and solve systems of linear equations by reducing them to their row echelon form.
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