1. Find Decompose(A,B,C)
`A=(1,2)`,`B=(3,1)`,`C=(8,1)`

Solution:
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
`1x+3y=8`

`2x+1y=1`

Solution of equations using Elimination method

Total Equations are `2`

`x+3y=8 -> (1)`

`2x+y=1 -> (2)`

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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)`

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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=-1vec (A) +3vec (B)`

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2. Find Decompose(A,B,C)
`A=(1,2)`,`B=(1,3)`,`C=(2,4)`

Solution:
Here `vec A=(1,2),vec B=(1,3),vec C=(2,4)`

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

So system of linear equations are
`x+y=2`

`2x+3y=4`

Solution of equations using Elimination method

Total Equations are `2`

`x+y=2 -> (1)`

`2x+3y=4 -> (2)`

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

`x+y=2`	` xx 2->`		``	`2x`	`+`	`2y`	`=`	`4`	``
		−
`2x+3y=4`	` xx 1->`		``	`2x`	`+`	`3y`	`=`	`4`	``
					`-`	`y`	`=`	`0`	` -> (3)`

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Now use back substitution method
From (3)
`-y=0`

`=>y=0`

From (1)
`x+y=2`

`=>x+(0)=2`

`=>x=2`

Solution using Elimination method.
`x = 2,y = 0`

`x=2,y=0`

So, `vec C = 2vec (A)`

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