Write as a Vector Equality y=x-3 , y=1+z , z=4-x

Problem

y=x−3,y=1+z,z=4−x

Solution

1. Rearrange each equation to isolate the constant term on one side, ensuring all variables x y and z are aligned.

x−y=3

y−z=1

x+z=4

2. Identify the coefficients of x y and z for each equation to form a system of linear equations.

1*x−1*y+0*z=3

0*x+1*y−1*z=1

1*x+0*y+1*z=4

3. Construct the vector equality by representing the system in the form A*v=b where A is the coefficient matrix, v is the vector of variables, and b is the vector of constants.

[[1,−1,0],[0,1,−1],[1,0,1]]*[[x],[y],[z]]=[[3],[1],[4]]

Final Answer

[[1,−1,0],[0,1,−1],[1,0,1]]*[[x],[y],[z]]=[[3],[1],[4]]

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