Write as a Vector Equality 5x+3y+z=-21 , x-3y+2z=-15 , 14x-2y+3z=60

Problem

{[5*x+3*y+z=−21],[x−3*y+2*z=−15],[14*x−2*y+3*z=60])

Solution

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

2. Express the system as a linear combination of these column vectors, where each variable acts as a scalar multiplier for its respective coefficient vector.

3. Set the sum of these scaled vectors equal to the vector of constants from the right-hand side of the equations.

Final Answer

x*[[5],[1],[14]]+y*[[3],[−3],[−2]]+z*[[1],[2],[3]]=[[−21],[−15],[60]]

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