#7. Given that the three 3-dimensional vectors v1 = (- 1,3, - 4), v2 = (3, – 8, 10), v3 = (2, – 9,7) are linearly independent (hence form a basis for R³), express the vector w = (1, – 14, 5) as a linear combination of these three vectors v1, v2, V3, checking that your answer really works.

Q: 2- We can write the vector x = (19,–1,–) in R³ as a linear %3D combination of the vectors x1 = (4,2,…

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Q: Find the coordinate vector [x]gof x relative to the given basis B= {b1,., bn}. -[-]»= [-{]==(:)

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Q: Find the coordinate vector of ?=(3,−7) relative to the basis ?={?1,?2} for ℝ2 if ?1=(1,1),?2=(0,2)

A: 1012 x = 3-71x = 3 and 1x + 2y = -7 Thus we get x = 3 Substitute in second equation, we get 2y = -10…

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Q: a) Find the vector orthogonal to the plane through the points P(2,-3,4), Q(-1, -2, 2), and R(3,1,…

A: equation of sphere centered at (h, k, j) and with radius R is: (x-h)2 + (y-k)2 + (z-j)2  =  R2 if A…

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A: To find- Calculate the first two vectors generated by the Jacobi method. -41013-10-15x = -6-67, x0 =…

Q: (i, 2, 3i), v = Co over C. Are these vectors linearly independent? Can they form a basis 5.…

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Q: 1 -1 6.5 [0] -2 10 7 3 x = 1 -4 10 -2 | 12.5] 3 3 10

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Q: Find the coordinate vector[x],of x relative to the given basis B= {bl,., bn}. --]--[}]--[1] bị = ,b2

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Q: Find the coordinate vector of p relative to the basis S = {p1, P2, P3 } for P2. p = 2 – 3x + 2x² ;…

A: Question from linear algebra.

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Q: i. Start with finding Two vectors u and v of R' which are linearly independent (you can see this by…

A: In the given question we have to find the the Linearly independent vectors in ℝ3. Concept: In a set…

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Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

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Q: 5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are…

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Q: (и, из) for Find the coordinate vector of w relative to the basis S R². Let ui (5, –4), u2 = (3, 7),…

A: Solvig by au+bv=w

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Q: 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0, -1] in R'. Decide whether they…

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Q: 9. V =|-1 Write the vector as the linear combination of the basis vectors 3 4 and u, =|- 3 u, = 2…

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A: Let x = v + wWhere v = a1u1 + a2u2 + a3u4        and w = a4u4.

Q: to = [0 3 4 2]" v = [1 1 2 1]"

A: Handwriting solution.  { v0, v1, e1, e4} forms a basis for R4.

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A: Here we have to find the linear combination.

Q: 1. Show that the following vectors are linearly dependent. Uz = U3= %3D -2 3.

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Q: Consider the following graph. (5, 5) 5 y 3 (1, 2) 1. 1 3 4 5 (a) Find the component form of the…

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Q: Find the coordinate vector of p(x) in P., relative to the basis S= {p,.P.-P;}, where p(x) =…

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Q: The z-coordinate of the terminal point of the vector v=-5i-19k whose initial point is (-1,-4,-5) is

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Q: 17 (c) Find a unit vector which is orthogonal to the vectors -1 2 and 1 -3 5

A: First we will find a vector which is orthogonal to both given vectors and then we will find the unit…

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Q: 3 Find the coordinates of y 7 relative to the orthogonal basis Uj = U2 = U3 = -2 -4 10 2 2 4 252

A: The solution is given as

Q: Find the coordinate vector of p = 2 – 4x relative to the basis B = {q,,q,} for P1 where q1 = 3 + 8x,…

A: Given : We are given a vector,  p = 2-4x  and a basis  B = q1, q2,                 where,  q1= 3+8x…

Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

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Q: 4 Suppose v1, V2, V3 are vectors in R*, and the matrix A = v, v2 V3 has rank 1 W = Span{v1, V2, V3}…

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Q: Q2. (d) Show that u=(-2,3,1,4) v=(1,2,0,-1) and are orthogonal vectors in R4.

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Q: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

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: Find a vector orthogonal to both v and W. v = 3i + 2j + k, w = -5i - 5j - k 3i - 2j - 5k -3i + 2j -…

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Q: Find the coordinate vector of v relative to the basis S = {v,, V2, V3} for R³. (b) v = (5, –12, 3);…

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Q: Find a vector orthogonal to (0, 1, 7) and (2i – j+ 4k) 11i + 14j - 2k 2i - j+ 11k -j + 28k 4i + 14j…

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Q: Find the coordinate vector of a -2 with respect to the basis B %3D for R.

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Q: 1 -1] 5 -4 2 1 -3 1 -2 -1 3 2 16

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Q: 4 Find the coordinate vector of b=|-2 relative to the ordered basis B= 1

A: The coordinate vector of a vector b = ( p, q, r )T realtive to the ordered basis B = { xT , yT , zT…

Q: Given vectors v1 = (3,0,0), v2 = (1,2,0), and v3 = (2,–4,5). 7.. a) Are the vectors linearly…

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Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: . Find the coordinates of the vector v relative to the ordered basis B. a) B = {x² + 2x +2, 2x…

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Q: Given vectors v1 = (3,0,0), v2 = (1,2,0), and v3 = a) Are the vectors linearly independent or…

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Q: Find the orthogonal projection of the vector b =-1 on Nul(A), where -2 -2 3 -10 A = 1 -1 2 3 1 -3 3…

A: For the solution follow the next steps.

Q: Find the coordinate vector for the vector v = (3,4,3) relative to the basis S={(3,2,1), (-2,1,0),…

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Q: Find the coordinates of vector u=(4,5) with respect to linear basis ((2,1),(1,-1) ? a. 2 b. 3 • 2 O…

A: Here we use linear combination to solve this