Write as a Vector Equality 3y+2z+w=1 , 2x+2y-2z+4w=2

Problem

{[3*y+2*z+w=1],[2*x+2*y−2*z+4*w=2])

Solution

1. Identify the variables and constants in the system of linear equations. The variables are x y z and w

2. Rewrite the equations to align the variables in columns, ensuring each variable is represented in both equations (using a coefficient of 0 if necessary).

0*x+3*y+2*z+1*w=1

2*x+2*y−2*z+4*w=2

3. Extract the coefficients of the variables to form a coefficient matrix and a vector of variables.

[[0,3,2,1],[2,2,−2,4]]*[[x],[y],[z],[w]]

4. Equate the product of the coefficient matrix and the variable vector to the vector of constants from the right-hand side of the equations.

Final Answer

[[0,3,2,1],[2,2,−2,4]]*[[x],[y],[z],[w]]=[[1],[2]]

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