1. Say whether the following vectors are linearly independent and whether the vectors form a basis of R³. Support your answers with reasons. (a) {(1,2,3), (-1,2,3)}. (b) (c) {(2,-2, 1), (0, 2, -2), (2, 0, -1)}. (d) {(1,2,3), (-1,2,3), (0, 0, 0)}. {(1, 1, 1), (1, −1, −1), (−1, 1, −1), (-1, -1, 1)}.

Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

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

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Q: 4. State with a brief explanation whether the following statements are true or false. (a) The…

A: a) true The vectors (1 ,0) and (0,1) is linearly independent. We know that linearly independent set…

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: The plane passing through the three points A(4, –3, –4), B(-4, –3,2) and C(-3,3, –2) can be…

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Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: Find the coordinate vector of p relative to the basis S = {P₁, P₂, P3 } for P₂. p = 15 - 20x + 6x²:…

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Q: 3. Determine which of the pairs of vectors are orthogonal. (a) a = (b) u = (c) y = 8 12 -5 3,0 = -3…

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Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of…

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Q: Find a vector equation for the line through the point (4, 5, -1) perpendicular to the vectors , 6,…

A: we have to find the line equation passing through point (4,5,-1) and perpendicular to the vectors…

Q: The initial and terminal points of a vector v are given. Terminal Initial Point Point (2/²) (14) (a)…

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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: Consider the following points. A(3, 1, 1), B(4, -4, 6), C(7, -2, 0), D(6, 3, −5) Let u = AB, VAC,…

A: Consider the following points.Let , , and . Find each of these vectors.Find the scalar triple…

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·A·B·0-0-0-0 x 3 +y -2 +2 1 = 1…

A: We want to find values of x, y and z which satisfy given equation.

Q: (d) Let w =(-39,22), v’i=(2–5), v°2=(5,-4), v°3=(-4,-1). If possible, express w as a linear…

A: In this question we need to multiply vectors by constant and have to find values of constant

Q: (a) Determine whether W= (0, 5, 4) can be expressed as a linear combination of the vectors v1 =…

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Q: The coordinate vector of the (-4,3,1) in the B={u= (1,1,1); v = (1,0,1); w=(0,0,1)} is : A. (-4,3,1)…

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Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

A: Given Data: Let us consider the given data, c 2,-2,1,0,2,-2,2,0,-1d 1,1,1,1,-1,-1,-1,1,-1,-1,-1,1…

Q: 3.2.1 Vector Cross Product Let vectors: A = (1, 0, −3), B = (–2, 5, 1), and C = (3, 1, 1). Part…

A: Since, you have posted a question with sub-parts greater than three. We will provide the solution…

Q: #7. Given that the three 3-dimensional vectors v1 = (- 1,3, - 4), v2 = (3, – 8, 10), v3 = (2, – 9,7)…

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Q: #1: a) Express v = (2,13,6) in R³ as a linear combination of the following vectors vị = (1, 5, – 1),…

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Q: Find the coordinate vector of v relative to the basis S = {v1, v2, V3} for R3. v = (-11,–17,7) V1 =…

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Q: Let a = 2 0 and b = 0 (9) 2 1 be two vectors. What is a|2|b2+|ab|²? [Please enter your answer…

A: Solution :- Given :a = -120 and b = 012a=-12+22=5a2=5b2=12+22=5b=5a.b =-1*0+2*1+0*2=2a.b2=22=4

Q: 2. Consider the vectors =(1,2,3,0),= (0,1,2,3) and = (2,3,4,-3) Let = (1,1,1,1) (a) Is a linear…

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Q: Let = (1,2) and 7=(3, a) be two vectors in R². (a) For which value of a the two vectors an are…

A: Vector is parallel to another iff one is constant multiple of other .example: u=kv Orthogonal when…

Q: Find a subset of the vectors that forms a basis of their span: (i) vi = (-1,1, -2,1), v2 = (2,-2,…

A: For (i), Notice that v2=2, -2, 4, -2=-2-1, 1, -2, 1=-2v1. So, the subset of the vectors that form a…