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

Problem

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

Solution

1. Rearrange the equations so that all terms containing variables are on the left side and constant terms are on the right side.

x+2*y+3*z=2

2*x+y+0*z=2

5*x+2*y+2*z=5

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

Coefficients of *x:([1],[2],[5])

Coefficients of *y:([2],[1],[2])

Coefficients of *z:([3],[0],[2])

3. Express the system as a linear combination of these column vectors equated to the constant vector.

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

Final Answer

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

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