Let u, v and w be three n-dimensional column vectors. We would like to compute r = uv¹w, which is also an n-dimensional vector. Justify your answer on which of the following sequence of computation is better: (uv)w or u(vw)?
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- Consider a vector ('L', 'M', 'M', 'L', 'H', 'M', 'H', 'H'), where H stands for ‘high’, L stands for ‘low’, and M for ‘medium’ in rstudio. a. Convert this vector into an unordered factor. b. Convert this vector into an ordered factor with Low < Medium < High.Let y be a column vector: y = [1, 2, 3, 4, 5, 6] so that y.shape = (6,1). Reshape the vector into a matrix z using the numpy.array.reshape and (numpy.array.transpose if necessary) to form a new matrix z whose first column is [1, 2, 3], and whose second column is [4, 5, 6]. Print out the resulting array z./*** We will assume that `matrixA` and `matrixB` are valid 2D arrays of* `int`s. Each matrix is rectangular, with each row having the same number* of columns.** First, we need to make sure the matrices are compatible. Given `numRows X* numColumns` for each matrix `A` and `B`, if `A` is `m x n`, then `B` must* be `n x p`. That is the ``inner`` dimensions (lengths) must match.** If number of columns in `matrixA` does NOT equal the number of rows in* `matrixB`, then return `null`. That is, not output is created.** Assuming the dimensions are consistent, then we create a 2D output array* that is `m x p`, that is `numRowsA X numColumnsB`.** To calculate each element of the output matrix, we multiply the rows of* `A` by the columns of `B` and sum them up.** For example, let for integer values be given by lower case letters, let* `A` be a 2 x 3 matrix, and `B` a 3 x 3 matrix. The inner dimensions are* consistent, so we can multiply.** <pre>[a, b ,c]A = [d, e, f][p, q, r]B = |s, t, u|[v,…
- Dont the matrix V,P dont need any value?Give a clear description of an efficient algorithm for finding the k smallest elements of a very large n-element vector. Compare its running time with that of other plausible ways of achieving the same result, including that of applying k times your solution for part (a). [Note that in part (a) the result of the function consists of one element, whereas here it consists of k elements. As above, you may assume for simplicity that all the elements of the vector are different.]Give a MPI program segment to convert a n-by-n matrix distributed on a n-by-n 2D mesh such that allits rows and columns get sorted in ascending order. Show only the iterative loop. Only communicationsallowed are to the four direct neighbors. (Hint: You may employ a variant of odd-even transpositionsort, but the whole matrix does not need to be sorted.)
- (20pts) Consider the matrixA =−2 11−10 5(a) Determine, by hand, an SVD of A, A = UΣVT. The SVD is not unique,so find the one with the minimum number of minus signs in U and V . List thesingular values σ1 and σ2, and the left and right singular vectors.(b) Find A−1 not directly, but via the SVD. Check your result by typing inv(A)in MATLAB or calculating A−1 by other methods.(c) Find the eigenvalues λ1 and λ2 of A. Verify that detA = λ1λ2 and |detA| =σ1σ2Write a matlab code for Creating 5x5 matrix with rank 4 and generate 2 vectors each that are not in a. Column space b. Rowspace c. Left null space d. Right null space Explain how will you verify your answer for various cases in above problemNeed Python code to graph f = sin(9x) to show the exact solution and the graphs of its interpolation using n = 12 (12 sub-intervals). T= 6. Also, using the same intervals plot its L2 projection. Print the (n+1)*(n+1) matrix M and the (n+1)*1 vector b. eed
- Consider the vector: x = c(1,2,3,4). What is the value of (x+2)[(!is.na(x)) & x > 0]? What do you find?Need Python code to graph f = sin(9x) to show the exact solution and the graphs of its interpolation using n = 12 (12 sub-intervals). T= 6. Also, using the same intervals plot its L2 projection. Print the (n+1)*(n+1) matrix M and the (n+1)*1 vector b.we represent the finite-length signals as vectors in Euclidean space, many operations on signals can be encoded as a matrix-vector multiplication. Consider for example a circular shift in C: a delay by one (i.e. a right shift) transforms the signal x = (xo X1 X2]" into x = [xı xo xz]" and it can be described by the matrix TO D = [0 1 0'0 0 1'1 0 0] so that x = Dx. Determine the matrix F that implements the one step difference operator in C ie the operator that transforms a signal x into [(x - x)(x1 - x0)(x2 - 1)]