Write as a Vector Equality 2x+3y-z=-1 , 6x+9y-3z=-3 , -2x-3y+2z=1

Problem

{[2*x+3*y−z=−1],[6*x+9*y−3*z=−3],[−2*x−3*y+2*z=1])

Solution

1. Identify the coefficients of the variables x y and z in each equation to form the column vectors for the left side of the equality.

2. Extract the constants from the right side of each equation to form the constant vector.

3. Express the system as a linear combination of vectors by multiplying each variable by its corresponding vector of coefficients.

4. Combine the vectors into a single vector equality where the sum of the scaled component vectors equals the constant vector.

Final Answer

x*[[2],[6],[−2]]+y*[[3],[9],[−3]]+z*[[−1],[−3],[2]]=[[−1],[−3],[1]]

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