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

Problem

{[3*x+y=−3],[x+y−z=−3],[2*x+5*y+z=0])

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 by multiplying each vector by its corresponding variable.

3. Set the linear combination equal to the vector of constants from the right-hand side of the equations.

4. Combine the components into the standard vector equation form x*(v_1)+y*(v_2)+z*(v_3)=b

Final Answer

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

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