Write as a Vector Equality x+y+z=5 , -2x-3y+2z=8 , 3x-y-2z=3

Problem

{[x+y+z=5],[−2*x−3*y+2*z=8],[3*x−y−2*z=3])

Solution

1. Identify the variables x y and z as the scalars that multiply the column vectors formed by the coefficients of each variable across the three equations.

2. Extract the coefficients for each variable to form the column vectors: the coefficients for x are 1, -2, 3;ƒ*o*ra*r*e, -3, -1;a*n*d(ƒ)*o*ra*r*e, 2, -2$.

3. Form the constant vector using the values on the right side of the equations: 5, 8, 3$.

4. Combine these into a single vector equation where the sum of the scaled column vectors equals the constant vector.

Final Answer

x*[[1],[−2],[3]]+y*[[1],[−3],[−1]]+z*[[1],[2],[−2]]=[[5],[8],[3]]

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