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Definition and examples
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Vector Algebra
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Vector Operation
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Linearly dependent and linearly independent vectors calculator |
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- `(1,2,3), (4,5,6),(7,8,9)`
- `(1,2,3), (2,4,6),(3,4,5)`
- `(5,-1,1), (-2,3,4),(3,4,5)`
- `(5,6,1), (0,2,3),(3,4,5)`
- `(1,2), (2,1)`
- `(1,2), (1,3),(2,4)`
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Decimal Place =
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Solution
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Solution provided by AtoZmath.com
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Linearly dependent and linearly independent vectors calculator
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 1. `(1,2), (2,1)`
2. `(1,2), (1,3),(2,4)`
3. `(1,2,3), (4,5,6),(7,8,9)`
4. `(1,2,3), (2,4,6),(3,4,5)`
5. `(5,-1,1), (-2,3,4),(3,4,5)`
6. `(5,6,1), (0,2,3),(3,4,5)`
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Example1. Find isLinearlyDependant(A,B,C)
`A=(1,2,3)`,`B=(4,5,6)`,`C=(7,8,9)`Solution:Here `vec A=(1,2,3),vec B=(4,5,6),vec C=(7,8,9)` The vectors A, B, C are linearly dependent, if their determinant is zero. i.e. `|D|=0` | `|D|` | = | | `1` | `2` | `3` | | | `4` | `5` | `6` | | | `7` | `8` | `9` | |
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`=1 xx (5 × 9 - 6 × 8) -2 xx (4 × 9 - 6 × 7) +3 xx (4 × 8 - 5 × 7)` `=1 xx (45 -48) -2 xx (36 -42) +3 xx (32 -35)` `=1 xx (-3) -2 xx (-6) +3 xx (-3)` `= -3 +12 -9` `=0` Since `|D|=0`, So vectors A, B, C are linearly dependent.
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