Write as a Vector Equality x+3y+5z=20 , y-4z=-16 , 3x-2y+9z=36

Problem

{[x+3*y+5*z=20],[y−4*z=−16],[3*x−2*y+9*z=36])

Solution

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

2. Express each equation as a linear combination of the variable vectors by grouping the coefficients of x y and z into separate column vectors.

3. Set the sum of these weighted vectors equal to the constant vector formed by the values on the right side of the equations.

Final Answer

x*[[1],[0],[3]]+y*[[3],[1],[−2]]+z*[[5],[−4],[9]]=[[20],[−16],[36]]

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