Which of the following subsets of R 3 are actually subspaces?(a) The plane of vectors (b1, b2, b3 ) with b1 = b2(b) The plane of vectors with b1 = 1.( c) The vectors with b1 b2 b3 = 0.(d) All linear combinations of v = (1, 4, 0) and w = (2, 2, 2).(e) All vectors that satisfy b1 + b2 + b3 = 0.(f) All vectors with b1 < b2  < b3

Q: Determine nonzero vectors that are orthogonal to the following vectors. (a) (1, 5)     (b) (6, −1)…

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Q: Let (3,-1,2) and (1,4,-1) be co-planar vectors(two vectors that sit in the same plane). Find a…

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Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

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Q: Find the equation of the line that passes tru the points (-1,-3) and (5,1)

A: Given points are: (-1,-3) and (5,1) Equation of line: y-y1=m(x-x1) Where (x1,y1)=(5,1) m=slope of…

Q: 5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3,2,1) (b)…

A: The objective of this question is to determine whether the given sets of vectors are dependent or…

Q: Below are 3 sets of 3-dimensional vectors: {}] (i) (ii) {}}} -8 (iii) 3 Determine which set(s)…

A: for the given sets of vectors

Q: 3. (a) Explain why there is no vector i such that (3, –1, 4) × J = (-5,1, –4). (b) Explain why there…

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Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

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Q: EXAΜPLE2 Determine whether the vectors vi-(1,-2,3),v2=(5,6,-1),v3-(3,2,1) are linearly independent…

A: Given vectors are v1 = (1, -2, 3), v2 = (5, 6, -1), v3 = (3, 2, 1)

Q: at vectors （c1 - a1, c2 - a2）and （b1-a1,b2-a2）are linearly depend

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

A: A set is linearly dependent if and only if one vector is linear combination of other vectors.

Q: Determine whether each collection of vectors is linearly independent or linearly dependent. Justify…

A: According expert guidelines of Bartleby I have to solve only first three subpart so repost for…

Q: 5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3, 2, 1) (b)…

A: The objective of this question is to determine whether the given sets of vectors are dependent or…

Q: Write each vector as a linear combination of the vectors in S. (Use s, and s2, respectively, for the…

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Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

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: Are the vectors V₁ = 2 1 1 V₂ = 1₂V3 3 4 1 linearly independent? -9

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.