Let T (V₁, V2, V3) w = (4, 1, −1). = (2v1 + V2, 2v2 − 3v₁, V₁ — V3). Find T(–4,5,1) and pre-image of

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: let v = (1, 3, −2) and w = (2, −1, 4). Compute v × w.

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Q: 5. x₁ + x₂ -3x1 3 +2x30 X₂ - 2x3 = 2

A: According to Bartley guidelines, these are separate questions. Please ask second question…

Q: 2.x - y-z = 0 5x - 2у +2: 3 Зх + у - 2: -8

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Q: Let p = 5x + 10x + 3. Find the coordinate vector of p relative to the following basis for P2, P1 =…

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Q: Find a least-squares best fit line for the points (1, 5), (2, 1), (3, 1), (4, 3). Write your answer…

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Q: Find all values a for which the set {(a — 5, 13, 0), (−1, a – 9,0), (4, 0, a — 2)} is linearly…

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Q: Determine: If S = {X2,1 + X2} is linearly independent or dependent.

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Q: EXER 3.2 - LINEAR ALGEBRA Write v =(4,4,5) as a linear combination of x=(1,2,3), y =(-2,0,1) and z =…

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Q: ) Let B = {vi =,₂ =, V3 =}. Determine whether B is linearly independent or linearly dependent.

A: Let us consider a set of vectors V=v1,v2,.......vn. The set of vectors are said to be linearly…

Q: Is T linear? If Yes find KerT, where T(x1, x2, x3) = (x1+x3, x1-x3, x2 )

A: Given Tx1,x2,x3=x1+x3,x1−x3,x2 We have to show that T is linear and then find the KerT Let…

Q: 5) Let 0 H 1 0 Can w be written as a linear combination of V1, V2, V3, and v4? V₁ = 2 V₂ = 2 3 1 and…

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Q: Let ui = (3, –1,3, 3), u2 = (-2,3, 1, 3), and uz = (0, –1, -1, –1). Write v = (8, –9, 1, –1) as a…

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Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: Consider the subset of P3 Q = {−6x² + 4x − 6, −24x² + sx + 6, 2sx + s} Find the two values of s for…

A: In this question, we will find the values of 's' for which a given set is linearly dependent.

Q: Find a least-squares best fit line for the points (1, 1), (2, 5), (3, 5). Write your answer as a…

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Q: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

A: According to the given information, it is required to find a linear dependence between the columns…

Q: The point (1,2-1) in space is inside the ball B((1,1,1);2).

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Q: Can we write v = (1,5,4) as a linear combination of u = (1,3, -2), uz = (2,7,-1), ug = (1,6,7) ?

A: If there exist a,b,c∈ℝ such that au1+bu2+cu3=v then we can say  v as a linear combination of u1,u2…

Q: Let u = (2, -1,3), v = (3,0,1) and w = (-1,-1,3). find all values of I, m and n such that lu + mv +…

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Q: For the data (-3,9), (-2,6), (0,2), and (1,1) find the line and the parabola that provide the least…

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Q: 1 [-1] 2 Let 2 , v2 0 ,V3 = where S = {v,,v,,v,}. %3D 3 Is V4 linear combination of V1, V2, V3?…

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Q: a. Is S = {v1, V2, V3} linearly independent

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Q: Show that the set S= {(20, 34), (40, 68)} is linearly independent or not?

A: Given set is S= {(20, 34), (40, 68)}

Q: Q7) True or False, and Justify your answer. If v1, v2, ... V4 are in Rª and v3 = 2v1 + v2, then…

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Q: Find w such that 2u + v – 3w = 0. u = (2, 7, 5, 0), v = (-3, 1, W =

A: Addition and subtraction of two vectors: Add or subtract the necessary components to add or subtract…

Q: 3. Find all real numbers t for V = (20 t,4t - 4,5t², t²) are orthogonal. - which = (1,5t,-4t, t³)…

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Q: 1 5 ]v s or fractions.) W = - 3 0

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Q: Let u = (−3,2,1,0), v = (4,7,−3,2), and w = (5, −2, 8, 1). Find the components of −u+(v−4w)

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Q: If u = [3, - 1] and v = [1,4],compute and draw u + v.

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Q: How is w = (-3, –13, 7) e R³ a linear combination of (0, -2, 2) and (1, 3, –1)? U = | V = O A. w =…

A: Given query is to find the correct option for linear combination.