Final answer:
To find the coordinate vector of a vector with respect to a basis, express the vector as a linear combination of the basis vectors and solve the system of equations.
Step-by-step explanation:
To find the coordinate vector of a vector with respect to a basis, we need to express the vector as a linear combination of the basis vectors. Let's say our vector is v = [v1, v2, v3] and the basis vectors are b1, b2, and b3.
Step 1:
Write the equation v = c1 * b1 + c2 * b2 + c3 * b3, where c1, c2, and c3 are the coefficients of the linear combination.
Step 2:
Solve the system of linear equations formed by equating the individual components of v to the corresponding components of the basis vectors.
Step 3:
The solution to the system of equations gives us the coordinate vector [c1, c2, c3].