Write as a Vector Equality (2/3)x+z=5 , y+(3/2)z=6 , 2x+3y=8

Problem

{[2/3*x+z=5],[y+3/2*z=6],[2*x+3*y=8])

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 coefficients for missing terms.

2/3*x+0*y+1*z=5

0*x+1*y+3/2*z=6

2*x+3*y+0*z=8

3. Express the system as a linear combination of constant vectors multiplied by the variables x y and z

x*[[2/3],[0],[2]]+y*[[0],[1],[3]]+z*[[1],[3/2],[0]]=[[5],[6],[8]]

4. Formulate the vector equality by representing the coefficients as a matrix multiplied by a column vector of variables.

[[2/3,0,1],[0,1,3/2],[2,3,0]]*[[x],[y],[z]]=[[5],[6],[8]]

Final Answer

[[2/3,0,1],[0,1,3/2],[2,3,0]]*[[x],[y],[z]]=[[5],[6],[8]]

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