for the system equation of x' = Ax if Coefficients Matrix A be ? = [...

for the system equation of x' = Ax if Coefficients Matrix A be ? = [ 5 −5 −5 −1 4 2 3 −5 −3 ] , find the basic matrix

Expert Solution

Colby Messinger answered 11 months ago

Suppose A is an n × n matrix with the property that the equation Ax =...

Suppose A is an n × n matrix with the property that the equation Ax = b has at least one solution for each b in R n . Explain why each equation Ax = b has in fact exactly one solution

Suppose the system AX = B is consistent and A is a 6x3 matrix. Suppose the...

Suppose the system AX = B is consistent and A is a 6x3 matrix. Suppose the maximum number of linearly independent rows in A is 3. Discuss: Is the solution of the system unique?

For matrices, a mulitplicative identity is a square matrix X such XA = AX = A...

For matrices, a mulitplicative identity is a square matrix X such XA = AX = A for any square matrix A. Prove that X must be the identity matrix. Prove that for any invertible matrix A, the inverse matrix must be unique. Hint: Assume that there are two inverses and then show that they much in fact be the same matrix. Prove Theorem which shows that Gauss-Jordan Elimination produces the inverse matrix for any invertible matrix A. Your proof cannot...

If an SPL ( LINEAR EQUATION SYSTEM ) is known: Ax = b. A is a...

If an SPL ( LINEAR EQUATION SYSTEM ) is known: Ax = b. A is a matrix sized m × n and b is a vector sized m × 1, with the component values of matrix A and vector b known. The x vector is n × 1 and the component values are unknown. Explain how the possible solution of SPL Ax = b. i want answer for the question , and what he mean by (the component values of...

y''-2ay'+a^2y=60xe^{ax}+60x^2e^{ax} Use the method of undetermined coefficients to find a particular solution for each equation. Then...

y''-2ay'+a^2y=60xe^{ax}+60x^2e^{ax} Use the method of undetermined coefficients to find a particular solution for each equation. Then solve each equation for real general solution. this is a non homogeneous differntial equation

A linear system of equations Ax=b is known, where A is a matrix of m by...

A linear system of equations Ax=b is known, where A is a matrix of m by n size, and the column vectors of A are linearly independent of each other. Please answer the following questions based on this assumption, please explain all questions, thank you~. (1) Please explain why this system has at most one solution. (2) To give an example, Ax=b is no solution. (3) According to the previous question, what kind of inference can be made to the...

Solve the linear system of equations Ax = b, and give the rank of the matrix...

Solve the linear system of equations Ax = b, and give the rank of the matrix A, where A = 1 1 1 -1 0 1 0 2 1 0 1 1 b = 1 2 3

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...

Let A be an m x n matrix. Prove that Ax = b has at least...

Let A be an m x n matrix. Prove that Ax = b has at least one solution for any b if and only if A has linearly independent rows. Let V be a vector space with dimension 3, and let V = span(u, v, w). Prove that u, v, w are linearly independent (in other words, you are being asked to show that u, v, w form a basis for V)

Given the differential equation (ax+b)2d2y/dx2+(ax+b)dy/dx+y=Q(x) show that the equations ax+b=et and t=ln(ax+b) reduces this equation to...

Given the differential equation (ax+b)2d2y/dx2+(ax+b)dy/dx+y=Q(x) show that the equations ax+b=et and t=ln(ax+b) reduces this equation to a linear equation with constant coefficients hence solve (1+x)2d2y/dx2+(1+x)dy /dx+ y=(2x+3)(2x+4)

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