A rectangular bookcase 60 inches long and 30 inches wide. How long is the diagonal? Round to the nearest inch.
2 answers:
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Since are linearly dependent, there exist coefficients
such that
Now, a linear combination of the new vectors would look like this:
Which simplifies to
So, any linear combination of is also a linear combination of
. This implies that we can choose the coefficients for a linear combination that will give the zero vector.
In particular, if are the coefficients such that
we can choose
And we have