### Video Transcript

Express the given set of simultaneous equations as a matrix equation. Three π₯ equals 12 plus five π¦ plus two π§, π₯ minus five π¦ equals 21, 11π₯ minus eight π¦ equals negative 10 plus two π§.

To solve this as a matrix equation, we need to get all of our variables lined up together. So letβs put each equation in the order of π₯, then π¦, then π§ equals a constant. Our first equation would be three π₯ minus five π¦ minus two π§ equals 12. Our next equation would be pretty much the same except there is no π§ term. So we have π₯ minus five π¦ plus zero π§ equals 21. And then our last equation will be 11π₯ minus eight π¦ minus two π§ equals negative 10.

To multiply matrices, we will take a row times a column. So weβll have three times π₯, negative five times π¦, and negative two times π§, would equal 12. That will be our first equation. Then we would have one times π₯, negative five times π¦, and zero times π§, equals 21. Thatβs our second equation. And then 11 times π₯, negative eight times π¦, negative two times π§, equals negative 10.

And this is how you would express these simultaneous equations as a matrix equation.