Write as a Vector Equality x+3y+z=a , x-2y+z=b , 3x+7y-z=c

Problem

{[x+3*y+z=a],[x−2*y+z=b],[3*x+7*y−z=c])

Solution

1. Identify the coefficients of the variables x y and z in each equation to form the columns of the coefficient matrix.

2. Define the variable vector as a column vector containing the unknowns x y and z

3. Define the constant vector as a column vector containing the values a b and c from the right side of the equations.

4. Construct the matrix equation by multiplying the coefficient matrix by the variable vector and setting it equal to the constant vector.

Final Answer

[[1,3,1],[1,−2,1],[3,7,−1]]*[[x],[y],[z]]=[[a],[b],[c]]

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