Write as a Vector Equality -2x+2y-10z=-6 , x-y+5z=3 , 5x-5y+25z=15

Problem

−2*x+2*y−10*z=−6,x−y+5*z=3,5*x−5*y+25*z=15

Solution

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

2. Define the vector of variables x as a column vector containing x y and z

3. Extract the constants from the right-hand side of each equation to form the constant vector b

4. Construct the vector equality in the form A*x=b by placing the coefficients into a 3×3 matrix and the constants into a 3×1 vector.

Final Answer

[[−2,2,−10],[1,−1,5],[5,−5,25]]*[[x],[y],[z]]=[[−6],[3],[15]]

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