MAS 4105—Fall 1994
Some common mistakes you shouldn’t make.
1. Expressions that do not have “=” signs in them are not equations. In particular:
•
A vector is not an equation.
•
A sum of vectors is not an equation.
•
A linear combination of vectors is not an equation.
•
An inequality is not an equation.
2. The word
solution
should be used correctly. Equations and inequalities can have
solutions. However,
•
A vector does not have a solution.
•
A matrix does not have a solution.
.
3. A
vector
is not the same thing as a
vector space
.
4. A
basis
is not the same thing as the vector space it’s a basis of.
5. A basis is not the same thing as a
linear combination
of vectors.
6. A basis is not the same thing as a
sum
of vectors.
7. A basis is not the same thing as a
solution set
to a system of linear equations.
8. A
set
of vectors is not the same thing as a
linear combination
of vectors.
9. A
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 Spring '09
 RUDYAK
 Linear Algebra, Vector Space, Elementary algebra, Linear combination

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