Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use s1, S2, and s3, respectively, for the vectors in the set.) S = {(1, 2, 3, 4), (1, 0, 1, 2), (3, 8, 11, 14)} (0, 0, 0, 0) = Express the vector s3 in the set as a linear combination of the vectors s, and s,. S3 =

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A: Given Two non-zero vectors a and b such that  a+b=a-b            ...........1 The dot product of and…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: Write the vector w = (1, 1, 1) as a linear combination of vectors in the set S. V2 V3 S = {(1, 2,…

A: See the attachment.

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Q: Show that vectors (86, 87, –46), (-8, –6, –2), and (-6, –7, 6) are linearly dependent-that is, there…

A: If vectors are linearly dependent then they can be expressed as a linear combination of each other

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Given S={ s1 = (2,-1,3),   s2 =(5,0,4)} a) To write (-1,-2,2) as linear  combination of s1 and s2

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A: we have to show that the set is linearly dependent by finding a nontrivial linear combination of…

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂…

A: Linear Combination:       A vector V is called a linear combination of vectors   v1, v2, . . ., vn…

Q: The figure shows a basis B = {bj,b2 } for R² and a vector v in R?. y b1 b2 Custom basis B = {b1, b2…

A: Let B={b1,b2} be a basis for ℝ2 and v∈ℝ2.

Q: (i) Prove that { (1, 2, 1) , (2, 1, 5) , (1, –4, 7) } is linear dependent subset of R³. (ii)…

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Q: 3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x,…

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A: The given set of vectors:  110 , b10 , 023

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Linear Combination