Write as a Vector Equality 9x+y=2 , y+z=0 , 6x-z=1

Problem

{[9*x+y=2],[y+z=0],[6*x−z=1])

Solution

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

2. Rewrite each equation to include all variables by using zero as a coefficient for missing terms.

9*x+1*y+0*z=2

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

6*x+0*y−1*z=1

3. Express the system as a linear combination of constant vectors multiplied by the variables.

x*[[9],[0],[6]]+y*[[1],[1],[0]]+z*[[0],[1],[−1]]=[[2],[0],[1]]

4. Formulate the vector equality by representing the coefficients as a matrix and the variables as a vector.

[[9,1,0],[0,1,1],[6,0,−1]]*[[x],[y],[z]]=[[2],[0],[1]]

Final Answer

[[9,1,0],[0,1,1],[6,0,−1]]*[[x],[y],[z]]=[[2],[0],[1]]

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