Write as a Vector Equality x+y+z=-3 , x-y+3z=5 , 5x+y+z=9

Problem

{[x+y+z=−3],[x−y+3*z=5],[5*x+y+z=9])

Solution

1. Identify the coefficients of the variables x y and z for each equation in the system.

2. Represent the system as a linear combination of constant vectors multiplied by the variables x y and z

3. Construct the vector equality by placing the coefficients of x into the first vector, the coefficients of y into the second vector, and the coefficients of z into the third vector.

4. Equate the sum of these vectors to the vector containing the constants from the right-hand side of the equations.

Final Answer

x*[[1],[1],[5]]+y*[[1],[−1],[1]]+z*[[1],[3],[1]]=[[−3],[5],[9]]

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