Write as a Vector Equality 3x-y=-15 , x+2y-z=1 , 2x+3y-2z=0

Problem

{[3*x−y=−15],[x+2*y−z=1],[2*x+3*y−2*z=0])

Solution

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

2. Extract the coefficients of x from each equation to create the first vector: ([3],[1],[2])

3. Extract the coefficients of y from each equation to create the second vector: ([−1],[2],[3])

4. Extract the coefficients of z from each equation to create the third vector: ([0],[−1],[−2])

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

Final Answer

x*([3],[1],[2])+y*([−1],[2],[3])+z*([0],[−1],[−2])=([−15],[1],[0])

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