Write as a Vector Equality 3x+5y-z=0 , 4x-y+2z=1 , 7x+4y+z=1

Problem

{[3*x+5*y−z=0],[4*x−y+2*z=1],[7*x+4*y+z=1])

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 the system to create the first vector: ([3],[4],[7])

3. Extract the y coefficients from the system to create the second vector: ([5],[−1],[4])

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

5. Identify the constants on the right side of the equations to form the result vector: ([0],[1],[1])

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

Final Answer

x*([3],[4],[7])+y*([5],[−1],[4])+z*([−1],[2],[1])=([0],[1],[1])

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