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 matrix)

Expert Solution

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Colby Messinger answered 2 years ago

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

2. (Solving linear systems) Consider the linear system Ax = b with A =[14 9 14...

2. (Solving linear systems) Consider the linear system Ax = b with A =[14 9 14 6 -10;-11 -11 5 8 6;15 -2 -14 8 -15;14 13 11 -3 -7;0 9 13 5 -14], and . b = [-4;8;6;0;10]. a) Verify that the linear system has a unique solution. Hint: use rref, rank, det, or any other Matlab method. Briefly explain the answer please. You'll now solve Ax = b in three different ways. Store the three different solutions in...

Write a function to solve a system of linear equations of the form Ax= b using...

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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)

Make the program(such as matlab) for solving the linear system Ax = b using the Naive-Gaussian...

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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

2.) By Theorem 3.23 of the text, the linear diophantine equation of the form ax +...

2.) By Theorem 3.23 of the text, the linear diophantine equation of the form ax + by = c has no integral solutions if c is not divisible by (a, b), the greatest common divisor of a and b. On the other hand if (a, b) divides c, then we can use the Extended Euclidean Algorithm to find integers s, t such that sa + tb = (a, b); multiplying through by the correct factor gives an integral solution x,...

(a) The n × n matrices A, B, C, and X satisfy the equation AX(B +...

(a) The n × n matrices A, B, C, and X satisfy the equation AX(B + CX) ?1 = C Write an expression for the matrix X in terms of A, B, and C. You may assume invertibility of any matrix when necessary. (b) Suppose D is a 3 × 5 matrix, E is a 5 × c matrix, and F is a 4 × d matrix. Find the values of c and d for which the statement “det(DEF) =...

Consider the linear transformation T : P1 → R^3 given by T(ax + b) = [a+b...

Consider the linear transformation T : P1 → R^3 given by T(ax + b) = [a+b a−b 2a] a) find the null space of T and a basis for it (b) Is T one-to-one? Explain (c) Determine if w = [−1 4 −6] is in the range of T (d) Find a basis for the range of T and its dimension (e) Is T onto? Explain

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