# Algebra 2 help! ?

I’ve been trying to figure out how to solve this bonus question and it doesn’t make sense. I think you solve using diagonals but I’m having trouble with solving Relevance
• Since column 1 = column 3, you immediately know that the determinant is 0. You can work it out like others did, and you should know now to do that, but for this particular problem there's no need for that.

It's always = 0 when the rows or the columns are not linearly independent.

• It's asking for the determinant of a 3x3 matrix.

Let's assume you had a matrix that was:

M = [a b c]

...... [d e f]

.......[g h i]

The determinant would be:

|M| = a(ei − fh) − b(di − fg) + c(dh − eg)

That may look complicated, but look at the picture below to see how you get there.

[d f d]

[1 1 1]

[f d f]

That will become:

d(1f - 1d) + f(1f - 1f) + d(1d - 1f)

= d(f - d) + 0 + d(d - f)

= d(f - d) - d(f - d)

= 0

0 • since the lines are | |

it is asking for the determinant

so for a 3 x 3 is it rather simple

d ( f -d) - f (f-f) + d ( d-f)