Write as a Vector Equality 2x+3y-4z=-13 , -x+3y+2z=-7 , 3x-2y+z=14

Problem

{[2*x+3*y−4*z=−13],[−x+3*y+2*z=−7],[3*x−2*y+z=14])

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 to create the first vector: ([2],[−1],[3])

3. Extract the coefficients of y to create the second vector: ([3],[3],[−2])

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

5. Set the linear combination of these vectors equal to the constant vector formed by the values on the right side of the equations.

Final Answer

x*([2],[−1],[3])+y*([3],[3],[−2])+z*([−4],[2],[1])=([−13],[−7],[14])

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