Linear Albegra Lecture 2 - Elimination with matrices

Linear Equations vs line and pland vs vectors.

Solve a system of equations with the method of elimination

I’ll do a subtraction. First of all this is the key number that I’m starting with. And that’s called the pivot.

…

Step 2

We found three pivots, and by the way, I didn’t say this, pivots can’t be 0. I don’t accept 0 as a pivot.

How could this have failed?

Element 1,1 could zero, then swap the row.

Element 2,2 be 6 could be trouble.

Element 3,3 be -4 coould be trouble.

Matrix x Columns = columns

Rows x Matrix = rows

Substraction matrix:

Substracti 3 times row 1 from row 2:

即 -3 * [1 2 1] + 1 * [3 8 1]

$$ (E_{32} E_{21}) A = U $$

Multiply on the left changes to rows.

Multiply on the right that changes swap the columns.

$$ E^{-1} E = I$$