2
$\begingroup$

In matrices, we justify row operations by drawing parallels with solving a system of equations i.e.:
1.Interchanging rows = Interchanging equations \

2.Adding one multiple of a row to another = Adding one multiple of an equation to another \

3.Multiplying all terms of a row by a constant = multiplying both sides of an equation by that constant.

Now, we can do much the same with columns as well. What's the logic supporting column operations? Can we draw a parallel to solving a system of equations for column operations as well? Thanks!

$\endgroup$
0
$\begingroup$

The system of equations traditionally represented by the matrix equation $A\overline x = b$ can also be represented by the equation $\overline x^tA^t = b^t$. Now the variable $\overline x^t$ is a row, it's the columns of $A^t$ that correspond to equations, and column operations correspond to elementary operations on the original system of equations.

So doing column operations on a matrix corresponds to doing elementary operations on the system of equations that is traditionally represented by the transpose of that matrix.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.