Write as a Vector Equality x-9y=z-17 , x=7+y-z , x+y-z=3

Problem

{[x−9*y=z−17],[x=7+y−z],[x+y−z=3])

Solution

1. Rearrange each equation into the standard form a*x+b*y+c*z=d by moving all variable terms to the left side and constants to the right side.

x−9*y−z=−17

x−y+z=7

x+y−z=3

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

Coefficients of *x:([1],[1],[1])

Coefficients of *y:([−9],[−1],[1])

Coefficients of *z:([−1],[1],[−1])

3. Express the system as a linear combination of these column vectors set equal to the vector of constants.

x*([1],[1],[1])+y*([−9],[−1],[1])+z*([−1],[1],[−1])=([−17],[7],[3])

Final Answer

x*([1],[1],[1])+y*([−9],[−1],[1])+z*([−1],[1],[−1])=([−17],[7],[3])

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