Write as a Vector Equality

Problem

{[a+b+2*d+g=1],[a−b−d+g=0],[b+d=−1],[a+b+g=2])

Solution

1. Identify the variables and their coefficients in each equation to represent the system as a linear combination of vectors.

2. Define the column vectors corresponding to each variable a,b,d,g by extracting the coefficients from the four equations.

3. Construct the vector equation by multiplying each variable by its respective coefficient vector and setting the sum equal to the vector of constants from the right-hand side.

4. Verify the components of the vectors:

a*([1],[1],[0],[1])+b*([1],[−1],[1],[1])+d*([2],[−1],[1],[0])+g*([1],[1],[0],[1])=([1],[0],[−1],[2])

Final Answer

a*([1],[1],[0],[1])+b*([1],[−1],[1],[1])+d*([2],[−1],[1],[0])+g*([1],[1],[0],[1])=([1],[0],[−1],[2])

Want more problems? Check here!