Linear Independence (Linear Algebra)
Free printable university Linear Algebra worksheet on deciding whether sets of vectors in R3 are linearly independent and finding explicit dependence relations.
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Linear Algebra · Math worksheet
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Linear Algebra: Linear Independence
Decide whether each set of vectors is linearly independent. If it is dependent, give an explicit dependence relation. Column vectors are written as [1; 2; 3].
- 1.Determine whether v1 = [2; -2; 4], v2 = [-3; 4; -1], v3 = [-4; 3; -4] are linearly independent in R³. If they are dependent, give a dependence relation.
- 2.Determine whether v1 = [3; 1; -3], v2 = [4; 3; 1], v3 = [10; 5; -5] are linearly independent in R³. If they are dependent, give a dependence relation.
- 3.Determine whether v1 = [-2; 0; 2] and v2 = [-4; 0; 4] are linearly independent in R³. If they are dependent, give a dependence relation.
- 4.Determine whether the four vectors v1 = [1; 3; 1], v2 = [-4; -4; -4], v3 = [2; -3; 0], v4 = [2; -2; -2] are linearly independent in R³.
- 5.Determine whether v1 = [2; 3; -4], v2 = [-1; -1; 4], v3 = [1; -3; 3] are linearly independent in R³. If they are dependent, give a dependence relation.
- 6.Determine whether v1 = [-4; 4; -3], v2 = [-1; 4; 3], v3 = [-14; 20; -3] are linearly independent in R³. If they are dependent, give a dependence relation.
- 7.Determine whether v1 = [2; -1; -1] and v2 = [3; -1; -3] are linearly independent in R³. If they are dependent, give a dependence relation.
- 8.Determine whether the four vectors v1 = [-1; 4; -2], v2 = [-2; 1; -4], v3 = [3; 3; -1], v4 = [-4; -2; 4] are linearly independent in R³.
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