Write as a Vector Equality x+2y-3z=5 , -y+4z=1 , 3x-4y+3x=-3

Problem

{[x+2*y−3*z=5],[−y+4*z=1],[3*x−4*y+3*z=−3])

Solution

1. Identify the variables in the system of linear equations, which are x y and z

2. Extract the coefficients from the left side of each equation to form a coefficient matrix A

3. Define a column vector x containing the variables x y and z

4. Extract the constants from the right side of each equation to form a constant vector b

5. Express the system in the form A*x=b where the matrix-vector product represents the linear combination of the columns.

Final Answer

[[1,2,−3],[0,−1,4],[3,−4,3]]*[[x],[y],[z]]=[[5],[1],[−3]]

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