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Solution
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Solution provided by AtoZmath.com
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Decomposition of vector in basis calculator
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 1. `(1,2), (3,1),(8,1)`
2. `(1,2), (1,3),(2,4)`
3. `(3,7), (-1,2),(3,20)`
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Example1. 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 methodTotal 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=-1vec (A) +3vec (B)`
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