1. Find Decompose(A,B,C)
`A=(3,7)`,`B=(-1,2)`,`C=(3,20)`

Solution:
Here `vec A=(3,7),vec B=(-1,2),vec C=(3,20)`


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

So system of linear equations are
`3x-1y=3`

`7x+2y=20`

Solution of equations using Elimination method

Total Equations are `2`

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

`7x+2y=20 -> (2)`

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

`3x-y=3`	` xx 2->`		``	`6x`	`-`	`2y`	`=`	`6`	``
		+
`7x+2y=20`	` xx 1->`		``	`7x`	`+`	`2y`	`=`	`20`	``
			``	`13x`			`=`	`26`	` -> (3)`

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Now use back substitution method
From (3)
`13x=26`

`=>x=(26)/(13)=2`

From (1)
`3x-y=3`

`=>3(2)-y=3`

`=>-y+6=3`

`=>-y=3-6=-3`

`=>y=3`

Solution using Elimination method.
`x=2,y=3`

`x=2,y=3`

So, `vec C=2vec (A) +3vec (B)` 2. Find DECOMPOSE(B,C,A)
`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 A = x vec B + y vec C`

So system of linear equations are
`3x+8y=1`

`x+y=2`

Solution of equations using Elimination method

Total Equations are `2`

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

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

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

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

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

`=>y=(-5)/(5)=-1`

From (2)
`x+y=2`

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

`=>x-1=2`

`=>x=2+1=3`

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

`x=3,y=-1`

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

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