Chapters

Vectors are linearly dependent if there is a linear combination of them that equals the zero vector, without the coefficients of the linear combination being zero.

Properties

1.If several vectors are linearly dependent, then at least one of them can be expressed as a linear combination of the others.

If a vector is a linear combination of others, then all the vectors are linearly dependent.

2.Two vectors are linearly dependent if, and only if they are parallel.

3.Two vectors = (u1, u2, u3) y = (v1, v2, v3) are linearly dependent if their components are proportional.

Example

Determine the values of k for the linearly dependent vectors , and . Also, write as a linear combination of and , where k is the calculated value.

The vectors are linearly dependent if the determinant of the matrix is zero, meaning that the rank of the matrix is less than 3.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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