Question

Consider the following coefficient matrix

A=[[3,1,-3],[2,2,2],[0,1,1]] and the vector b=[[2],[4],[2]]
a) which form the equation system Ax=b

Answer 1

To solve the equation system Ax=b, we can use Gaussian elimination. The solutions for x are x = [[-1], [1], [1]].

Step-by-step explanation:

The given equation system is Ax = b, where A is the coefficient matrix and b is the vector. In this case, A = [[3, 1, -3], [2, 2, 2], [0, 1, 1]] and b = [[2], [4], [2]]. To solve this system, we need to find the values of x that satisfy the equation.

To do this, we can use Gaussian elimination or matrix inversion. Let's use Gaussian elimination:

1. Write the augmented matrix by combining A and b: [[3, 1, -3 | 2], [2, 2, 2 | 4], [0, 1, 1 | 2]].
2. Perform row operations to get the matrix in row echelon form.
3. Back-substitute the values to find the solutions for x.

The solutions for x are x = [[-1], [1], [1]].