Write as a Vector Equality x+y+z=0 , x-y+5z=20 , 5x+y+z=4

Problem

{[x+y+z=0],[x−y+5*z=20],[5*x+y+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 coefficients of x from each equation to create the first vector: ([1],[1],[5])

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

4. Extract the coefficients of z from each equation to create the third vector: ([1],[5],[1])

5. Identify the constants on the right side of the equations to form the result vector: ([0],[20],[4])

6. Combine these into a single vector equation where the variables scale their respective coefficient vectors.

Final Answer

x*([1],[1],[5])+y*([1],[−1],[1])+z*([1],[5],[1])=([0],[20],[4])

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