## For what values of h are the vectors [Start 3 By 1 Matrix 1st Row 1st Column negative 1 2nd Row 1st Column 4 3rd Row 1st Column 6 EndMatrix

Question

For what values of h are the vectors [Start 3 By 1 Matrix 1st Row 1st Column negative 1 2nd Row 1st Column 4 3rd Row 1st Column 6 EndMatrix ]​, [Start 3 By 1 Matrix 1st Row 1st Column 5 2nd Row 1st Column 2 3rd Row 1st Column negative 3 EndMatrix ]​, [Start 3 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column negative 5 3rd Row 1st Column negative 4 EndMatrix ]​, and [Start 3 By 1 Matrix 1st Row 1st Column 12 2nd Row 1st Column negative 20 3rd Row 1st Column h EndMatrix ]linearly​ dependent?

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1 day 2021-09-15T03:21:41+00:00 1 Answer 0 Since the determinant is not zero, this implies that the vectors a,b,c are all linearly independent. Since a,b,c are all vectors in which is a 3-dimensional space, and they are 3 linear independent vectors, then they are automatically a base of this space. Consider now the vector d. Since {a,b,c} is a base of , then it generates any vector of this space(i.e any other vector of the space is a linear combination of {a,b,c}). In particular, d. So the set {a,b,c,d} is linearly independent for any value of h