Write as a Vector Equality y=3x , -3x+y=0

Problem

y=3*x,−3*x+y=0

Solution

1. Identify the variables and the structure of the system. The equations represent a relationship between x and y that can be expressed as a linear combination of vectors.

2. Rewrite the equation −3*x+y=0 in terms of a vector dot product or a linear combination.

3. Express the variables x and y as a vector ([x],[y])

4. Determine the scalar relationship. Since y=3*x any vector satisfying this must be a scalar multiple of a basis vector where the second component is three times the first.

5. Formulate the vector equality by pulling the variable x out as a scalar.

Final Answer

([x],[y])=x*([1],[3])

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