Final answer:
The question pertains to linear algebra, where the goal is to find the vectors in R⁴ that transform into a zero vector under transformation x→Ax for a given matrix A. This can be done by converting the matrix to its reduced row echelon form and solving for the system of linear equations. This process eventually leads to the identification of vectors that transform into zero under given matrix mapping.
Step-by-step explanation:
In the field of mathematics, specifically linear algebra, the task is to find out all the vectors x in R⁴ that when mapped by the transformation x→Ax result in zero vector or null space. The matrix A given here is: [1 2 9 -1] [1 0 3 -5] [0 1 3 4] [-2 4 5 18]. We are looking for the solution to the equation Ax = 0. In order to solve for x, we need to reduce the matrix A to its reduced row echelon form (RREF) and solve for x: