Matrices row reduction

Just a quick question
Does multiplying a row by a constant change the matrice, like for example row swapping when doing row reduction changes it to a negative

Reply 1

ghostwalker

Original post by /revisionqueen

Just a quick question
Does multiplying a row by a constant change the matrice, like for example row swapping when doing row reduction changes it to a negative

I presume you're talking about the determinant of a matrix, since you mention row swapping mutliplies it by -1.

If you multiply a row by a constant, then the determinant is multipled by that constant.

Reply 2

/revisionqueen

Thank you.Yes I meant determinant of a matrix.
So for this example if I needed to get a 1 instead of a three then the determinant outside would be a 1/3.

Reply 3

ghostwalker

Original post by /revisionqueen

Thank you.Yes I meant determinant of a matrix.
So for this example if I needed to get a 1 instead of a three then the determinant outside would be a 1/3.

First off, a matrix is usually written with oversized parentheses around it, whereas a determinant is written with vertical straight lines, so all those in your working should be the latter.

If you want a "1" as the middle element, then you take out a factor of 3 as in standard factorisation, to get 3|...|.

Note: you need to divide the whole row by 3, not just your desired element.

Reply 4

/revisionqueen

Thank you for the help :smile:

I will amend my working out
I got the det(A) as 1

(edited 1 year ago)

Reply 5

ghostwalker

Original post by /revisionqueen

Thank you for the help :smile:

I will amend my working out
I got the det(A) as 1

Agreed.

Reply 6

/revisionqueen

For this 4x4 matrix to get a 1 in the 2s place, would I need to take the 2 out.Would that make it -1(2)?

Reply 7

ghostwalker

Original post by /revisionqueen

For this 4x4 matrix to get a 1 in the 2s place, would I need to take the 2 out.Would that make it -1(2)?

Regarding your question, yes, if you want to get a 1 in your circled position.

Note: Your first determinant on the right looks to have an error in row3 column2.

(edited 1 year ago)

Reply 8

/revisionqueen

Oh yes, that was a mistake it should be a -1

Reply 9

ghostwalker

Original post by /revisionqueen

Oh yes, that was a mistake it should be a -1

If this is an exercise in row reduction, fine, but it's all about working out determinants, then I would have started by expanding your initial determinant down the 3rd column, as it would reduce the problem to a 3x3 determinant; though only if it's something you've already covered in your class/textbook.

(edited 1 year ago)

Reply 10

/revisionqueen

No it’s an exercise in row reduction.
Though I think I messed up somewhere because the answer says it is 39 but I got -192.I can’t seem to spot the mistake.

Reply 11

ghostwalker

Original post by /revisionqueen

No it’s an exercise in row reduction.
Though I think I messed up somewhere because the answer says it is 39 but I got -192.I can’t seem to spot the mistake.