Recent content by emira

Homework Statement For the sequence defined recursively as follows: a_1 = 2, and a_(n+1) = 1/ (a_n)^2 for all n from N. Homework Equations So, we are supposed to use induction to first fidn if the sequence increases or decreases, and then use induction again to show if it...

Homework Statement Suppose that the sequence {a_n} converges to A. Define the sequence {b_n} by: b_n = (a_n +a_(n+1) )/2 Does the sequence {b_n} converge? If so, specify the limit and prove your conclusion. Otherwise, give an example when this is not true. Homework Equations...

What does x as a real number have to do with it though? what we have to prove is that the infinite intersection of this semi-intervals that get smaller and smaller, is an empty set. plus how could i prove that x is not an element of the small interval, and how does that help me into proving...

Homework Statement Prove that: ⋂_(n=1)^∞▒〖(0,1/n]=∅〗 Homework Equations If tried with mathematical induction, we would need to know the procedure follows: This would be my P(n) statement: ⋂_(n=1)^∞▒〖(0,1/n]=∅〗 now we would need to find out if P(1) is true and then assume...

But the product of the identity matrix with matrix zero is matrix zero, thus not giving me the matrix i started with. does that it mean the matrix is not decompos-able?

Homework Statement 0 0 1 1 0 0 0 1 0 decompose this matrix using LU decomposition. Homework Equations The Attempt at a Solution I took this matrix and augmented it with a zero (3 by 3) matrix. Then I performed the same row operations on both...the row operations with the...

Homework Statement Prove that: A is a subset of B if and only if (A intersection B)=A Homework Equations The Attempt at a SolutionI tried proving the right side, that is (A \cap B)=A For two sets to be equal then they have to be subsets of each other...so: (A \cap B)...