WEBVTT
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Express the given set of simultaneous equations as a matrix equation.
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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§.
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To solve this as a matrix equation, we need to get all of our variables lined up together.
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So letβs put each equation in the order of π₯, then π¦, then π§ equals a constant.
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Our first equation would be three π₯ minus five π¦ minus two π§ equals 12.
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Our next equation would be pretty much the same except there is no π§ term.
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So we have π₯ minus five π¦ plus zero π§ equals 21.
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And then our last equation will be 11π₯ minus eight π¦ minus two π§ equals negative 10.
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To multiply matrices, we will take a row times a column.
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So weβll have three times π₯, negative five times π¦, and negative two times π§, would equal 12.
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That will be our first equation.
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Then we would have one times π₯, negative five times π¦, and zero times π§, equals 21.
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Thatβs our second equation.
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And then 11 times π₯, negative eight times π¦, negative two times π§, equals negative 10.
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And this is how you would express these simultaneous equations as a matrix equation.