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MindTap Engineering for Glover/Overbye/Sarma's Power System Analysis and Design, 6th Edition, [Instant Access], 1 term (6 months)
6th Edition
ISBN: 9781305636309
Author: J. Duncan Glover; Thomas Overbye; Mulukutla S. Sarma
Publisher: Cengage Learning US
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Chapter 6, Problem 6.2MCQ
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H.W Find the Adjoint to the following matrix
0.5
X =
-1
-0.8
2.2
2
-3.3
The method to compress an image in image
processing is using convolution matrix where the
number of outputs is reduced by replacing the matrix
multiplication with much smaller kernel matrix. This
is illustrated on the figure below. In this example a
black and white photograph is scanned as a
rectangular array of pixels and then stored as image
matrix on the left by assigning each pixel a numerical
value in accordance with its gray level, (0 = white to
255 = black), then the entries in the matrix are
integers between O and 255.Then multiplication is
employed with much smaller kernel matrix in the
middle.
0|0 21 00 o
106
85
71
1
250 231 127 63
1
250 252 250 209 56
1
250 252 250 250 83
Kernel
0 0 0
Feature map
Image
Boxes in red and blue frames indicate how the upper
left element is formed by applying the kernel to the
corresponding upper left region of the input matrix.
The elements of much smaller "feature map" matrix
on the right can be calculated from:
3.
Write a phyton program that solves the following given problems:
1. Perform Matrix Addition. Add matrix [A] and [B]
Chapter 6 Solutions
MindTap Engineering for Glover/Overbye/Sarma's Power System Analysis and Design, 6th Edition, [Instant Access], 1 term (6 months)
Ch. 6 - For a set of linear algebraic equations in matrix...Ch. 6 - For an NN square matrix A, in (N1) steps, the...Ch. 6 - Prob. 6.9MCQCh. 6 - Prob. 6.11MCQCh. 6 - Using Gauss elimination, solve the following...Ch. 6 - Prob. 6.9PCh. 6 - Determine the bus admittance matrix (Ybus) for the...Ch. 6 - Prob. 6.34PCh. 6 - Prob. 6.37PCh. 6 - Prob. 6.38P
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- Given a 4 x 4 matrix, we have to interchange the elements of first and last row and show the resulting matrix in C++. Examples : Input: 3 4 5 0 26 12 27 12 2 1 1 2 Output: 2 1 1 2 26 12 27 12 3 450 Input: 9 7 5 1 2 3 4 1 5 6 6 5 1 2 3 1 Output: 1 2 3 1 2 3 4 1 5 6 6 5 975 1arrow_forwardStrassen's algorithm of matrix multiplication works faster than standard matrix multiplication ________ a by replacing the original matrix with a low dimensional matrix b by reducing number of sub-problems in its recurrence relation c by increasing number of multiplication d by avoiding calculation of some element in the resultant matrixarrow_forwardWrite a phyton program that solves the following given problems: 1. Perform Matrix Multiplication. Multiply matrix [A] and [B]arrow_forward
- Write a phyton program that solves the following given problems: 1. Perform Matrix Inversion for matrix [A] and [B]arrow_forwardMatrix multiplication plays an important role in a number of applications. Two matrices can only be multiplied if the number of columns of the fi rst matrix is equal to the number of rows in the second.Let’s assume we have an m × n matrix A and we want to multiply it by an n × p matrix B. We can express their product as an m × p matrix denoted by AB (or A ⋅ B). If we assign C = AB, and ci,j denotes the entry in C at position (i, j), then for each element i and j with 1 ≤ i ≤ m and 1 ≤ j ≤ p. Now we want to see if we can parallelize the computation of C. Assume that matrices are laid out in memory sequentially as follows: a1,1, a2,1, a3,1, a4,1, ..., etc.Assume that we are going to compute C on both a single core shared memory machine and a 4-core shared-memory machine. Compute the speedup we would expect to obtain on the 4-core machine, ignoring any memory issues.Repeat above Exercise, assuming that updates to C incur a cache miss due to false sharing when consecutive elements are in a…arrow_forwardDraw the following graph as represented in the adjacency matrix below. a b c d A 1 1 1 0 B 0 1 1 0 C 0 0 1 1 d 0 0 0 1arrow_forward
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- We are given a code symmetry, that takes an n x n matrix as its argument. It returns true if the matrix is symmetric and false if it is not. The run time of the code is calculated by counting how many times the /= comparison is executed. procedure symmetry(M) for x:=1 to (n-1) for y:=(i+1) to n if mxy /= myx then return false else return true (a) Calculate the best case run time for symmetry (will be a number). (b) Calculate the worst case run time for symmetry (will be a polynomial in n, it will be helpful to draw matrices of different sizes and compare the number of comparisons to find a pattern). (c) Determine the worst case run time in big O notation (d) Using the following definition of big O notation, prove the answer to (c) Definition: Let f and g be functions from the set of integers or the set of real numbers to the set of real numbers. We say that f(x) is O(g(x)) if there are constants C and k such that whenever x > k. [This is…arrow_forwardFind the generalized time functions of the following code snippet Matrics_Multiplication (A, B) { // nx m matrix A // m x p matrix B // n×p matrix C // C= AB 1. Let C be a new matrix of the appropriate size 2. For i from 1 to n: For j from 1 to p: 3. 4. Let sum = 0 For k from 1 to m: 5. Set sum + sum + Ajk × Bj 6. 7. Set Cj - sum 8. Return C }arrow_forwardSparse matrix-vector multiplication in Python is similar to numpy.dot operation, however the provided @ operator is used. Let us consider multiplying a 5 by 5 sparse matrix with a 5 by 3 sparse matrix shown below. 01000 00010 10001 10000 01000 100 001 x 000 010 100 The Python code to implement multiplication of these two sparse matricesarrow_forward
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