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Hi.
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In this video, we're going to solve a system of linear equations using augmented matrices.
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So the system that we're solving is 2x1 minus x2 equals 5 and x1 plus 3x2 equals 6.
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And so the way we do this using augmented matrices is we first establish this first matrix, which if you see is just the coefficients of our system.
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And then we add on the right hand side in the right hand column here.
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So we have 2, negative 1, 5, 1, 3, 6.
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And that's how we get our first matrix.
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Now, what we want, the end goal is to get this matrix that has 1s on the diagonal and 0 everywhere else.
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So the first thing we do to do that is we first make this entry at 0.
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So what we do is we do a linear combination.
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We say row two is going to be equal to row two minus half of row one.
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So in this entry here, we have one minus two times a half, which is zero.
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So we get a zero there...