Write as a Vector Equality x+y+z=7 , x+y-6z=14 , -6x+y+z=0

Problem

{[x+y+z=7],[x+y−6*z=14],[−6*x+y+z=0])

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],[−6])

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

4. Extract the coefficients of z from each equation to create the third vector: ([1],[−6],[1])

5. Identify the constants on the right side of the equations to form the result vector: ([7],[14],[0])

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

Final Answer

x*([1],[1],[−6])+y*([1],[1],[1])+z*([1],[−6],[1])=([7],[14],[0])

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