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Problem: Decomposition of vector (1,2),(3,1),(8,1) [ Calculator, Method and examples ]

Solution:
Your problem -> Decomposition of vector (1,2),(3,1),(8,1)

Here vec A=(1,2),vec B=(3,1),vec C=(8,1)

Form equation from vectors
vec C = x vec A + y vec B

So system of linear equations are
x+3y=8

2x+y=1

Solution of equations using Elimination method

Total Equations are 2

x+3y=8 -> (1)

2x+y=1 -> (2)

Select the equations (1) and (2), and eliminate the variable x.

 x+3y=8  xx 2->  2x + 6y = 16  − 2x+y=1  xx 1->  2x + y = 1   5y = 15  -> (3)

Now use back substitution method
From (3)
5y=15

=>y=(15)/(5)=3

From (1)
x+3y=8

=>x+3(3)=8

=>x+9=8

=>x=8-9=-1

Solution using Elimination method.
x = -1,y = 3

x=-1,y=3

So, vec C = -vec (A) +3vec (B)

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