Write as a Vector Equality x+3y+z=2 , -2x+2y-4z=-1 , -y+3z=1

Problem

{[x+3*y+z=2],[−2*x+2*y−4*z=−1],[−y+3*z=1])

Solution

1. Identify the coefficients for each variable x y and z in the system of linear equations.

2. Represent the system as a linear combination of vectors by grouping the coefficients of each variable into separate column vectors.

3. Include the constant terms from the right side of the equations as the resulting vector on the right side of the equality.

4. Construct the final vector equation by multiplying each variable by its corresponding coefficient vector.

Final Answer

x*[[1],[−2],[0]]+y*[[3],[2],[−1]]+z*[[1],[−4],[3]]=[[2],[−1],[1]]

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