Question

What is the result of adding row 1 to row 3 and then row 3 to row 1 in a matrix?

Answer 1

When adding row 1 to row 3 and then row 3 to row 1 in a matrix, the result is obtained by multiplying row 1 by 2 and adding it to itself.

Step-by-step explanation:

When adding row 1 to row 3 and then row 3 to row 1 in a matrix, we are performing the same operation twice, which means the result will be the same as adding row 1 to itself. This is equivalent to multiplying row 1 by 2 and then adding it to row 1.

For example, let's say we have a matrix:

1 2 3

4 5 6

7 8 9

Adding row 1 to row 3 means the third row will become:

8 10 12

Adding row 3 to row 1 again will be:

9 12 15

So the result of adding row 1 to row 3 and then row 3 to row 1 is:

9 12 15