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Form R 3

Form R 3

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determine if the vectors from a basis for R 3 basis means the collection should be linearly independent and that collection should spend our three so our three sir spend our three that means any vector in r3 should be a linear combination of this collection vectors okay so in Part A we got three vectors so to check if they are linearly independent we can just do the row reduction of the corresponding vector matrix let me put that in matrix so first column 1 1 0 2 3 0 1 2 3 so we do the row reduction and if we have pivot in each column that means these vectors are linearly independent okay let's see that so we're gonna make this hard to 0 q is a pivot so we're gonna make this 0 so all work on r2 so r2 minus r1 okay so 1 2 1 0 0 3 oh it's already simplified 1 minus 1 0 3 minus 2 1 2 minus 1 1 now if we look at closely we got pivot here on the first column pivot here second column pivot here and third column that means these three vectors are linearly independent at the same time we can s

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