Write as a Vector Equality x+y-3z=9 , -3x+5y+z=7 , x-y+4z=0

Problem

{[x+y−3*z=9],[−3*x+5*y+z=7],[x−y+4*z=0])

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 column of coefficients to create the first term of the vector sum.

x*[[1],[−3],[1]]

3. Extract the variable y from the second column of coefficients to create the second term.

y*[[1],[5],[−1]]

4. Extract the variable z from the third column of coefficients to create the third term.

z*[[−3],[1],[4]]

5. Equate the sum of these vectors to the vector containing the constants from the right side of the equations.

[[9],[7],[0]]

Final Answer

x*[[1],[−3],[1]]+y*[[1],[5],[−1]]+z*[[−3],[1],[4]]=[[9],[7],[0]]

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