Write as a Vector Equality 2x-y-3z=7 , 3x+y+z=10 , 5x+y+2z=15

Problem

{[2*x−y−3*z=7],[3*x+y+z=10],[5*x+y+2*z=15])

Solution

1. Identify the coefficients of the variables x y and z for each equation in the system.

2. Express the system as a linear combination of constant vectors, where each vector corresponds to the coefficients of a single variable.

x*[[2],[3],[5]]+y*[[−1],[1],[1]]+z*[[−3],[1],[2]]=[[7],[10],[15]]

3. Rewrite the linear combination as a single vector equality by performing scalar multiplication and vector addition on the left side.

[[2*x−y−3*z],[3*x+y+z],[5*x+y+2*z]]=[[7],[10],[15]]

Final Answer

[[2*x−y−3*z],[3*x+y+z],[5*x+y+2*z]]=[[7],[10],[15]]

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