Final answer:
To find all values of x that are mapped to the zero vector by a matrix a, one needs to solve the homogeneous system of linear equations ax = 0 to find the null space of the matrix. This is typically done through row reduction and finding a parameterized solution.
Step-by-step explanation:
The question is asking to find all values of x that are transformed into the zero vector by a given matrix, labeled as matrix a. To solve this, we would typically set up an equation where matrix a times a vector x equals the zero vector. Since the provided solution states '0 = 4', which seems to be a typo or irrelevant information, we cannot directly use it to find the values of x without more context. However, speaking generally, finding the values of x usually involves solving a system of linear equations derived from the matrix-vector product ax = 0, where a is the given matrix and x is the vector of variables we're solving for. The set of all such vectors x that satisfy this equation forms the null space or kernel of the matrix.
The solution process involves row reducing the augmented matrix of a followed by zero, if needed, and then finding the parameterized solution that represents all vectors, x, in the null space. This typically requires knowledge of linear algebra and matrix operations.