Linearly Dependant Calculatorwith Interval Calculator

What is Linear Dependence?

In linear algebra, a set of vectors is linearly dependent if at least one of the vectors can be defined as a linear combination of the others. This means there exists a non-trivial solution to the equation:

For example, in 2D space, vectors (1, 2) and (2, 4) are linearly dependent because (2, 4) = 2*(1, 2).

Interval Calculator

Interval arithmetic provides bounds for calculations with uncertain inputs. For two intervals [a, b] and [c, d], the basic operations are:

• Addition: [a + c, b + d]
• Subtraction: [a - d, b - c]
• Multiplication: [min(ac, ad, bc, bd), max(ac, ad, bc, bd)]
• Division: [min(a/c, a/d, b/c, b/d), max(a/c, a/d, b/c, b/d)] (c and d ≠ 0)

This calculator performs these operations and checks for linear dependence of interval vectors.

How to Use This Calculator

1. Enter the number of vectors you want to check for linear dependence
2. For each vector, enter the components separated by commas
3. For interval calculations, enter the lower and upper bounds of each component
4. Click "Calculate" to see the results

Examples

Linear Dependence Example

Vectors (1, 2) and (2, 4) are linearly dependent because:

Interval Arithmetic Example

For intervals [1, 3] and [2, 4], the sum is [3, 7] and the product is [2, 12].