Three vectors V₁, V₂, and v3 are given. If they are linearly independent, show this; otherwise, find a nontrivial linear combination of them that is equal to the zero vector. 2 -⠀ V3 = 9 V₁0 V₂ = -9 2 3 9 Select the correct answer below, and fill in the answer box(es) to complete your choice. ⒸA. The vectors V₁, V2, and V3 are linearly independent. The augmented matrix [V₁ V₂ V3 0] has an echelon form E = the trivial solution. (Type an integer or simplified fraction for each matrix element.) OB. The vectors V₁, V₂, and v3 are linearly dependent, because 3v₁ + ( )√₂ + ( ) √3 = 0 (Type integers or fractions.) V3 0. which has only

Illustrate with an example and a diagram why a+b=6+a¯ for all vectors a and b

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Determine if b is a linear combination of the other vectors. If so, express b as a linear combination. (If b cannot be written as a linear combination of the other two vectors, enter DNE in both answer blanks.) a = a, = b = Jas + ( 2 b =

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Given vectors a = (3, -5) and b = (-2, 7), find 4a - 5b

State the vector that is represented by the following graph. -4 -3 -2 -1 3 2 1 0 -1 1