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Suppose matrix Ais transformed into matrix Bby means of an elementary row operation. Is there an elementary row operation that transforms Binto A? Explain.

Short Answer

Expert verified

For transforming the matrix B into A we can do the inverse of operations that we have used for transforming the matrix A into B.

Step by step solution

01

Row operation

In matrix there are three type of row operation for transforming the matrix:

  1. Swapping the rows: In this operation we can swap any row with any other row.
  2. Constant multiplications with row: In this operation we can multiply any non-zero scalar with any row.
  3. Subtracting or adding the row: In this operation we can subtract or add another row.
02

Transforming A into B matrix

Suppose we have two matrixes A and B. For transforming the matrix A to B we can use three operations.

We can do swapping the rows likeRi↔Rj.

We can divide the row by scalar k like Ri→Rik.

We can add the row like Ri→Ri-kRj.

03

Transforming B into A matrix

For transforming the matrix B into A we can do the inverse of operation that we have used for transforming the matrix A into B.

If we have used swapping the rows likeRi↔Rj we can do the inverse like Rj↔Ri.

If we have used divide the row by scalar k likeRi→Rik we can do the inverse like.

Rj→Rik

If we have used adding the row likeRi→Ri-kRj we can do the inverse like Rj→Rj-kRi.

Hence, for transforming the matrix B into A we can do the inverse of operations that we have used for transforming the matrix A into B.

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