can a vector with dimensions R^N and a vector with dimensions R^N+1 be a matrix? and...

can a vector with dimensions R^N and a vector with dimensions R^N+1 be a matrix? and if so what would it dimension size be?

Expert Solution

Colby Messinger answered 1 year ago

maximumST is a function that should take an n × n vector (representing the adjacency matrix...

maximumST is a function that should take an n × n vector (representing the adjacency matrix of a graph) as input and return the value of the maximum spanning tree of the graph defined by the n × n vector. Code: #include <vector> #include <cmath> #include <iostream> #include <cstdio> using namespace std; double maximumST( vector< vector<double> > adjacencyMatrix ){ vector<int> row(4,-1); vector< vector<int> > matrix(5,row); cerr << matrix.size() << endl; cerr << matrix[0].size() << endl; for( int i = 0;...

4. The product y = Ax of an m × n matrix A times a vector...

4. The product y = Ax of an m × n matrix A times a vector x = (x1, x2, . . . , xn) T can be computed row-wise as y = [A(1,:)*x; A(2,:)*x; ... ;A(m,:)*x]; that is y(1) = A(1,:)*x y(2) = A(2,:)*x ... y(m) = A(m,:)*x Write a function M-file that takes as input a matrix A and a vector x, and as output gives the product y = Ax by row, as defined above (Hint: use...

Let A ∈ Mat n×n(R) be a real square matrix. (a) Suppose that A is symmetric,...

Let A ∈ Mat n×n(R) be a real square matrix. (a) Suppose that A is symmetric, positive semi-definite, and orthogonal. Prove that A is the identity matrix. (b) Suppose that A satisfies A = −A^T . Prove that if λ ∈ C is an eigenvalue of A, then λ¯ = −λ. From now on, we assume that A is idempotent, i.e. A^2 = A. (c) Prove that if λ is an eigenvalue of A, then λ is equal to 0...

4. The product y = Ax of an m n matrix A times a vector x...

4. The product y = Ax of an m n matrix A times a vector x = (x1; x2; : : : ; xn)T can be computed row-wise as y = [A(1,:)*x; A(2,:)*x; ... ;A(m,:)*x]; that is y(1) = A(1,:)*x y(2) = A(2,:)*x ... y(m) = A(m,:)*x Write a function M-file that takes as input a matrix A and a vector x, and as output gives the product y = Ax by row, as denoted above (Hint: use a for...

Show that R-1(a)R(a) = I, where I is the identity matrix and R(a) is the rotation matrix.

Show that R-1(a)R(a) = I, where I is the identity matrix and R(a) is the rotation matrix. This equation shows that the inverse coordinate transformation returns you to the original coordinate system.

Let A be a m × n matrix with entries in R. Recall that the row...

Let A be a m × n matrix with entries in R. Recall that the row rank of A means the dimension of the subspace in RN spanned by the rows of A (viewed as vectors in Rn), and the column rank means that of the subspace in Rm spanned by the columns of A (viewed as vectors in Rm). (a) Prove that n = (column rank of A) + dim S, where the set S is the solution space...

In R: write a function that inputs a vector x and a number n and returns...

In R: write a function that inputs a vector x and a number n and returns the first n elements of x. When n is greater than length(x), your function should just return x. We are not allowed to use any control flow statements

Linear Algebra we know that x ∈ R^n is a nonzero vector and C is a...

Linear Algebra we know that x ∈ R^n is a nonzero vector and C is a real number. find all values of C such that ( In − Cxx^T ) is nonsingular and find its inverse knowing that its inverse is of the same form

How to proof: Matrix A have a size of m×n, and the rank is r. How...

How to proof: Matrix A have a size of m×n, and the rank is r. How can we rigorous proof that the dimension of column space are always equal to the dimensional of row space? (I can use many examples to show this work, but how to proof rigorously?)

Suppose C is a m × n matrix and A is a n × m matrix....

Suppose C is a m × n matrix and A is a n × m matrix. Assume CA = Im (Im is the m × m identity matrix). Consider the n × m system Ax = b. 1. Show that if this system is consistent then the solution is unique. 2. If C = [0 ?5 1 3 0 ?1] and A = [2 ?3 1 ?2 6 10] ,, find x (if it exists) when (a) b =[1...

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