Vector and matrices are the independent or dependent

In summary, the conversation discusses determining whether three vectors (v1, v2, and v3) are independent or dependent. The task is to find the span of these vectors and explain why a given vector (W) is not in the span. The suggested approach is to use the definition of linear independence and show work to determine the status of the vectors.
  • #1
kiamax
5
0
Vector and matrices...are the independent or dependent

Homework Statement



Determine whether the vectors v1=[1,-1;0,0],v2=[2,-2;1,... and v3=[-5,5;1,0] are independent or dependent. Find the span {v1,v2,v3} and give a description. Explain why W = [4,4;4,4,] is not in the span {v1,v2,v3}.

Homework Equations


I have tried solving this problem in matrix form...I'm not sure if this is the correct way



The Attempt at a Solution


Please help
 
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  • #2


Use the definition of linear independence to show the vectors are independent, or show that they're dependent by writing one as a linear combination of the others. You need to show some work here before people will help.
 

1. Are vectors and matrices independent or dependent?

Vectors and matrices can be either independent or dependent, depending on the context in which they are being used. In general, vectors and matrices are considered independent if they have different dimensions, meaning they have a different number of elements. However, they can also be considered dependent if they are related by a mathematical operation, such as matrix multiplication.

2. How can I tell if a vector and matrix are independent or dependent?

To determine if a vector and matrix are independent or dependent, you can compare their dimensions. If they have different dimensions, they are independent. If they have the same dimensions, they may be dependent and you will need to further analyze their relationship through mathematical operations.

3. Can a vector and matrix be both independent and dependent?

No, a vector and matrix cannot be both independent and dependent at the same time. They will either have different dimensions and be independent, or have the same dimensions and be dependent.

4. How are vectors and matrices used in scientific research?

Vectors and matrices are commonly used in scientific research for data analysis, mathematical modeling, and simulation. They are especially useful in fields such as physics, engineering, and computer science where data and equations can be represented and manipulated in vector and matrix form.

5. Are there any real-life applications of vectors and matrices?

Yes, there are many real-life applications of vectors and matrices. They are used in fields such as economics, finance, and statistics for data analysis and forecasting. They are also used in computer graphics and animation for 3D transformations and transformations of objects. Additionally, they are used in machine learning and artificial intelligence for data processing and pattern recognition.

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