What are the components of u-w?

Thread starter catcat6088
Start date Nov 4, 2012
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Linear Linear dependence Vectors

In summary, a vector in linear algebra is a mathematical object with both magnitude and direction. Linear dependence is the property of a set of vectors where one or more vectors can be expressed as a linear combination of the others. Linear independence refers to a set of vectors that cannot be expressed as a linear combination of each other. To determine if a set of vectors is linearly dependent, one can find the determinant of the matrix formed by the vectors. Linear dependence is significant in vector spaces because it helps determine if a set of vectors spans the entire space and can simplify calculations and problem solving.

Nov 4, 2012

catcat6088

Let u=[1 2 3]T , v=[2 -3 1]T , and w=[3 2 -1]T. Find the components of
a) u-w
b) 7v+3
c) -w+v
d) 3(u-7v)
e) -3v-8w
f) 2v-(u+w)

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Nov 4, 2012

mfb

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Insights Author

Do you know how vectors are added?
If no, look in the script or a book.
If yes, where do you get problems?

Nov 4, 2012

catcat6088

can you give me the answer of part a? Because I forget how to do it

1. What is a vector in linear algebra?

A vector in linear algebra is a mathematical object that has both magnitude and direction. It can be represented as a list of numbers or coordinates in a particular coordinate system.

2. How is linear dependence defined?

Linear dependence is defined as the property of a set of vectors where one or more vectors in the set can be expressed as a linear combination of the other vectors. In other words, one vector can be written as a sum of scalar multiples of the other vectors.

3. What is the difference between linear independence and linear dependence?

Linear independence refers to a set of vectors that cannot be expressed as a linear combination of each other. In contrast, linear dependence means that one or more vectors can be written as a linear combination of the other vectors in the set.

4. How can you determine if a set of vectors is linearly dependent?

A set of vectors is linearly dependent if at least one vector can be expressed as a linear combination of the other vectors in the set. This can be determined by finding the determinant of the matrix formed by the vectors. If the determinant is equal to zero, the vectors are linearly dependent.

5. What is the significance of linear dependence in vector spaces?

Linear dependence is an important concept in vector spaces because it allows us to determine if a set of vectors spans the entire space. If a set of vectors is linearly dependent, it means that some of the vectors are redundant and do not contribute to the span of the space. This can help simplify calculations and make solving problems easier.