Write as a Vector Equality x+y+z=2 , -x+3y+2z=8 , 4x+y+0z=4

Problem

{[x+y+z=2],[−x+3*y+2*z=8],[4*x+y+0*z=4])

Solution

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

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

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

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

5. Identify the constants on the right side of the equations to form the result vector: ([2],[8],[4])

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

Final Answer

x*([1],[−1],[4])+y*([1],[3],[1])+z*([1],[2],[0])=([2],[8],[4])

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