linear dependence

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7 Terms

1
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If a matrix has more columns than rows, its columns are linearly dependent.

True

2
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Any set of vectors that includes the zero vector is linearly dependent.

True

3
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If the determinant of a square matrix is zero, its columns are linearly independent.

False

4
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Three vectors in ( \mathbb{R}^2 ) are always linearly dependent.

True

5
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A set of vectors is linearly independent if none of them can be written as a combination of the others.

True

6
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If the rank of a matrix is less than the number of columns, the columns are linearly independent.

False

7
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If a matrix has a column of all zeros, then its columns are linearly dependent.

True