Write as a Vector Equality x+y+z=6 , x-y+z=4 , 3x-2y+2z=13

Problem

{[x+y+z=6],[x−y+z=4],[3*x−2*y+2*z=13])

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: ([1],[1],[3])

3. Extract the coefficients of y from each equation to create the second vector: ([1],[−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: ([6],[4],[13])

6. Combine these into a single vector equation where each variable scales its respective coefficient vector.

Final Answer

x*([1],[1],[3])+y*([1],[−1],[−2])+z*([1],[1],[2])=([6],[4],[13])

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