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In this problem we have been asked to use determinants to determine if the given set of vectors is linearly independent.
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So first of all, let's find the determinant of the matrix whose columns are the given vectors.
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So the first vector is 1, 2, 5.
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Then we have negative 2, negative 1, 1.
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Then we have 1, 0, 1.
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We are going to find this determinant.
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Now to find this, let us expand this determinant along this column.
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And we're going to do that because we have a zero here.
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So that's going to make the calculations easier.
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So we have 1 times what? well, we remove the row and column that 1 is in.
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And we're going to consider this determinant.
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So we have 2 times 1 minus of minus 1 times 5.
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So this is what we get.
00:44
Then we have minus of 0...