Wikipedia
linear dependence and independence : The covariance is sometimes called a measure of "linear dependence" between two random variables. ..... More from Wikipedia
There is a linear relationship between the dependent variable and the ..
There is a linear relationship between the dependent variable and the independent variables. This is called the ________ assumption. The independent variables are not correlated. This is called the _______ assumption. => nonmulticolinearity, linearity..
Independent Events
Events are said to be independent if the occurrence of one event does not affect the occurrence of others. Observe in case(a) of above example, The probability of getting a white ball in the second draw does not depend on the occurrence of the event on the first draw. However i..
Events are said to be independent if the occurrence of one event does not affect the occurrence of others. Observe in case(a) of above example, The probability of getting a white ball in the second draw does not depend on the occurrence of the event on the first draw. However i.. More examples determining linear dependence or independence.
Linear Algebra: Introduction to linear dependence and independence
Question : i have a set of vectors:
v1 = i + 2j + 3k
v2 = 4i + 5j + 6k
v3 = 7i + 8j
i have to find if a vector in this set can be written as a linear combination of the two other vectors. I put the set into an augmented matrix and converted to RREF, but my third row is 0 0 9 0, so the matrix is undefined. I am confised as to whether this suggests linear dependence or independence....please help
Answer : I am not sure If I did something different but I got the rref as: 1000 0100 0010 I just did it on my calculator, and this would suggest linear independence since the rref did not render a free variable... More from Yahoo Answers
Answer : I am not sure If I did something different but I got the rref as: 1000 0100 0010 I just did it on my calculator, and this would suggest linear independence since the rref did not render a free variable... More from Yahoo Answers
Question : everyone says that if a1,a2, a3 ...aN are scalers and v1,v2,v3....vN are vectors then a1*v1+a2*v2+......aNvN=0;;;
what is the reason behind this perticular equation???
Answer : I believe they set the LHS of the equation to 0 and then try to find solutions. If there is only one solutions, then the vectors or independant. If there are more than one solutions, the vectors are dependant. A good way to think about it is to imagine three vectors in 2-dimensional space. You already know the two linearly independant vectors span 2d space( one in the x diection and one in the y direction) so the third vector is unecessary and must be linearly dependant on the other two. That means that you can find an equations such that v3=a1v1+a2v2. the a1 and a2 just change the size of the vectors and then when you add then you get v3... More from Yahoo Answers
Answer : I believe they set the LHS of the equation to 0 and then try to find solutions. If there is only one solutions, then the vectors or independant. If there are more than one solutions, the vectors are dependant. A good way to think about it is to imagine three vectors in 2-dimensional space. You already know the two linearly independant vectors span 2d space( one in the x diection and one in the y direction) so the third vector is unecessary and must be linearly dependant on the other two. That means that you can find an equations such that v3=a1v1+a2v2. the a1 and a2 just change the size of the vectors and then when you add then you get v3... More from Yahoo Answers
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