Write as a Vector Equality 2x-y+z=3 , x+y-3z=0 , 3x-2y+5z=5

Problem

{[2*x−y+z=3],[x+y−3*z=0],[3*x−2*y+5*z=5])

Solution

1. Identify the coefficients of the variables x y and z in 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.

3. Set the linear combination equal to the vector formed by the constants on the right side of the equations.

Final Answer

x*[[2],[1],[3]]+y*[[−1],[1],[−2]]+z*[[1],[−3],[5]]=[[3],[0],[5]]

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