Question

Homogeneous Equations: Problem 10 (1 point) Let A=[14​28​−5−20​14​] Describe all solutions of Ax=0. You have attempted this problem 0 times. You have unlimited attempts remaining.

Answer 1

To solve Ax=0 for the given matrix A, employ Gaussian elimination to find the reduced row-echelon form and determine the set of solutions, which could be either a trivial solution or infinitely many based on the presence of free variables.

Step-by-step explanation:

To describe all solutions of Ax=0 for the given matrix A, we first need to form the augmented matrix and then apply row reduction techniques to find the reduced row-echelon form (RREF). The given matrix is A=[14​2 8​​ ​ -5 -20​14​]. Apply Gaussian elimination to reduce the matrix and solve for x in Ax=0.

If the RREF of A has any rows of zeros and there are free variables, then the system has infinitely many solutions where the free variables can take any real values. Otherwise, if there are no free variables or rows of zeroes, then the only solution is the trivial solution, which is the zero vector.After we apply reduction techniques to the given matrix A, we can find the values for the variable vector x that satisfy the equation.