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

Problem

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

Solution

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

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

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

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

5. Identify the constants on the right side of the equations to form the result vector: ([3],[0],[3])

6. Combine these into a linear combination where the variables scale their respective coefficient vectors.

Final Answer

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

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