Write as a Vector Equality x-4y=11 , 3y+z=9 , -x+z=7

Problem

{[x−4*y=11],[3*y+z=9],[−x+z=7])

Solution

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

2. Rewrite each equation to include all variables by using zero coefficients for missing terms.

1*x−4*y+0*z=11

0*x+3*y+1*z=9

−1*x+0*y+1*z=7

3. Separate the system into a linear combination of constant vectors multiplied by each variable.

x*[[1],[0],[−1]]+y*[[−4],[3],[0]]+z*[[0],[1],[1]]=[[11],[9],[7]]

4. Express the system as a single vector equality in the form A*x=b by grouping the coefficients into a matrix and the variables into a column vector.

Final Answer

[[1,−4,0],[0,3,1],[−1,0,1]]*[[x],[y],[z]]=[[11],[9],[7]]

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