Video: Expressing a Set of Simultaneous Equations as a Matrix Equation

Express the given set of simultaneous equations as a matrix equation. 3π‘₯ = 12 + 5𝑦 + 2𝑧, π‘₯ βˆ’ 5𝑦 = 21, 11π‘₯ βˆ’ 8𝑦 = βˆ’10 + 2𝑧.

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Video Transcript

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

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

To multiply matrices, we will take a row times a column. So we’ll have three times π‘₯, negative five times 𝑦, and negative two times 𝑧, would equal 12. That will be our first equation. Then we would have one times π‘₯, negative five times 𝑦, and zero times 𝑧, equals 21. That’s our second equation. And then 11 times π‘₯, negative eight times 𝑦, negative two times 𝑧, equals negative 10.

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

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