WHY WOULD IT BE NON SENSE TO ASK FOR THE BASIS AND DIMENSION FOR X-3Y+5Z=7?
To determine the basis and dimension of a set of vectors, we typically deal with a vector space, not an equation. In the provided question, the equation x - 3y + 5z = 7 represents a single plane in three-dimensional space.
To find the basis and dimension of a set of vectors, we need to work with a set of vectors that satisfy certain conditions. For example, the basis of a vector space is a set of linearly independent vectors that span the entire space when combined through linear combinations.
In the given equation, x - 3y + 5z = 7, there are infinitely many solutions that satisfy the equation since it represents a plane. However, we cannot determine a basis or dimension from this equation alone.
To find the basis and dimension of a vector space, you would typically be given a set of vectors and asked to analyze their linear dependence or independence. The equation provided does not give us the necessary information to find the basis and dimension.