The text provided does not contain any spelling or typographical errors.
Added by Michael W.
Close
Step 1
Step 1: Claim the statement is false; give a counterexample. Show more…
Show all steps
Your feedback will help us improve your experience
Supreeta N and 86 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Consider the problem of finding an optimum local multiple alignment of the three sequences: X = X1 X2 ......Xn1 Y = Y1 Y2 ......Yn2 Z = Z1 Z2 ......Zn3. You are given a linear scoring scheme (α,β,γ) where α, β, γ ∈ {A, C, G, T, -}. In other words, the match scores and gap penalties are built into a 5×5×5 array, and the contribution to the total score if α in sequence X aligns with β in sequence Y and γ in sequence Z is s(α,β,γ). You may further assume that s(α,β,γ) < 0 whenever any of α, β, or γ is a gap. Write out, in pseudo-code, the algorithm for the generalization of the Smith-Waterman algorithm to this situation. Your pseudo-code should be under three headings: 1. Initialisation: with the formula for initializing the array F(i,j,k) on the 'boundary' i, j, or k = 0 of the cubic array. 2. Iteration: with the formula for iterating the array F(i,j,k). 3. Traceback: indicating how to determine the optimum score from the array and where to trace the alignment back to.
Supreeta N.
Find value , Here the function is discontinuous for each value of x given in the limit of the function. Be sure P(x) = When the limit approaches Select the correct choice below and, if necessary, comma the answer separate both answers within your choice needed; is discontinuous over the interval. The limit does not exist (Type your answer not exceeding 8 and interval notation) discontinuous at the single value *= is continuous values not extend Discontinuous The values Hit for the same value +5 Initial limit Infinite value G is continuous discontinuous to Value The limits both values do not exist and are not G value= The limit for larger value does not exist discontinuous over the interval. The limit is (Type your answer in interval notation) is discontinuous at the value of Discontinuous at the single value in the limit is smaller value does not exist and limit for any value k
Andrew N.
Consider a sequence of real-numbers r1, r2, ..., rN such that no two numbers are equal. Using these numbers, we create an (N x N) square matrix R such that the (i, j)-th element of R is given by ai,j = rk, where k = min(i, j), for i ≥ j. The elements ai,j are arbitrary for i < j. The indices i and j take values over the range 1, 2, ..., N. A. Let N = 5. Write elements of matrix (5 ! 5) R in terms of real-numbers r1, r2, ..., rN and other arbitrary values. Clearly, show the top 4 ! 4 part and all the elements on four corners. [20 points] B. Is R a symmetric matrix? Give reason for your answer. If the answer is no, what conditions should the elements above the main diagonal satisfy to make R a symmetric matrix. [10 points] C. Carry out appropriate EROs to reduce the matrix R to its echlon form. Is echlon form unique? Give at least two different versions of echlon form if your answer is no. [30 points] D. Starting from the echlon form in C, carry out EROs to reduce the matrix R to its row echlon form. Is row echlon form unique? Give at least two different versions of row echlon form if your answer is no. [10 points] E. Starting from the row echlon form in D, describe EROs to reduce the matrix R to its reduced row echlon form. There is no need to carry out these EROs. [10 points] F. State conditions for a unique solution to exist for the linear system Rx = b in terms of its echlon form derived in C. Give justification. [10 points] G. Now, b = [0 0 ... 0]T, an all-0 column vector. Study the linear system Rx = b. In terms of echlon form derived in C, state conditions for multiple solutions to exist. [10 points] H. Consider ERO1, namely exchange of two rows of matrix A. Let B be the matrix obtained after the ERO1 is performed on A. Find a matrix T such that B = T A. [OPTIONAL]
Adi S.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD