Write as a Vector Equality 3x-x+2x=3 , -x+3x-2x=-1 , 2x+2x+3x=14

Problem

{[3*(x_1)−(x_2)+2*(x_3)=3],[−(x_1)+3*(x_2)−2*(x_3)=−1],[2*(x_1)+2*(x_2)+3*(x_3)=14])

Solution

1. Identify the variables in the system of linear equations. Since the variables are all written as x we distinguish them by their positions as (x_1) (x_2) and (x_3)

2. Extract the coefficients of each variable to form column vectors. The coefficients for (x_1) are 3, -1, 2;ƒ*o*r_2t*h*e*y*a*r*e1, 3, 2;a*n*d(ƒ)*o*r_3t*h*e*y*a*r*e, -2, 3$.

3. Isolate the constants on the right side of the equations into a single constant vector. The constants are 3, -1, 14$.

4. Construct the vector equality by multiplying each variable by its corresponding coefficient vector and setting their sum equal to the constant vector.

Final Answer

(x_1)*[[3],[−1],[2]]+(x_2)*[[−1],[3],[2]]+(x_3)*[[2],[−2],[3]]=[[3],[−1],[14]]

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