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

Problem

{[x+y+z=3],[−x+3*y+z=8],[4*x+y=4])

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],[4])

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

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

5. Set the linear combination of these vectors equal to the constant vector from the right-hand side of the equations.

Final Answer

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

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