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

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


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)


From (1)




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


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

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