Write as a Vector Equality 2x+y+3z=13 , x+2y=11 , 3x+z=10

Problem

{[2*x+y+3*z=13],[x+2*y=11],[3*x+z=10])

Solution

1. Identify the coefficients of the variables x y and z for each equation in the system.

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

3. Construct the vector for x using the coefficients (2,1,3) the vector for y using (1,2,0) and the vector for z using (3,0,1)

4. Equate the sum of these scaled vectors to the constant vector (13,11,10) to form the vector equality.

Final Answer

x*[[2],[1],[3]]+y*[[1],[2],[0]]+z*[[3],[0],[1]]=[[13],[11],[10]]

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