Linear Algebra question This question is intended to be quite difficult, and I a

Question

Linear Algebra question

This question is intended to be quite difficult, and I am using it to practice but unfortunately have been struggling. Please if you could help, that would be amazing. Thank you so much! Also, this is all the information I was given on the question. Thank you again. I look forward to learning from you.

5. Consider a discretization of the interval (0,1) given by the points below (0,1/10, 2/10, 3/10,4/10, 5/10, 6/10, 7/10, 8/10, 9/10, 1). Let B where (r) 10 is the nodal Lagrangian basis for the space of piecewise linear functions on the discretization given above as we have described it in class. (a) What is 0 B?

Explanation / Answer

For part (a) , the answer is simple.

In any space of real valued functions forming a vector space V, the 0 function,

that is 0 (x) =0 throughout , is the 0 element of the vector space.

In this case , note that the function 0 is piecewise linear , since it is linear throughout the interval [0,1]

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