Write as a Vector Equality 2x+y-3z=0 , 4x+5y+z=8 , -2x-y+4z=2

Problem

{[2*x+y−3*z=0],[4*x+5*y+z=8],[−2*x−y+4*z=2])

Solution

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

2. Extract the variable x from the first terms of each equation to create the first vector component x*([2],[4],[−2])

3. Extract the variable y from the second terms of each equation to create the second vector component y*([1],[5],[−1])

4. Extract the variable z from the third terms of each equation to create the third vector component z*([−3],[1],[4])

5. Equate the sum of these scaled vectors to the vector formed by the constants on the right side of the equations.

Final Answer

x*([2],[4],[−2])+y*([1],[5],[−1])+z*([−3],[1],[4])=([0],[8],[2])

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