Show that {u₁, u2} is an orthogonal basis for R². Then express x as a linear combination of the u's. 2 12 2 པཏཱ = Աշ = and x = 6 -2

Q: ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

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Q: Write the vector v = B - - -3 8 5 -44] 50 24 1 - as a coordinate vector with respect to the basis

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Q: show two nonzero vectors a and b in the 5th dimensions. put them in vector form and in basis form.…

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Q: Explain why the vectors U₁=(3, 8, -8) U₂ = (-12, -32, 32) form a linearly dependent set of vectors…

A: Linearly dependent vectors

Q: Prove that the vectors (1,1,0), (3,1,3) and (5,3,3) are linearly dependent.

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Q: state a vector with all non-zero entries which is orthogonal to v⃗

A: Given v vector  Let w vector be orthogonal to v vector  Then w vector . v vector = 0

Q: Write the vector v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

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Q: The projection of the vector 5î + 5ĵ – 5k onto the vector –4î + 2ĵ – 4k. | |

A: We have to find out

Q: Show that {u,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the…

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Q: "Write x as the sum of two vectors, one in Span (u,.u₂.3), and one in Span (U4). Assume that (u) is…

A: In this question , we will write the 'x' as linear combination of remaining vectors .

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: Find the vector projection of v = -6i + 10j – konto w = = 2i + j − k (Give your answer using…

A: The given two vectors are  v=-6i+10j-k  and w=2i+j-k

Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: Show that the vectors a, (1, 0, 0), a2 = (1, 1,0), a, = (1, 1, 1) form a basis of C'(C).

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Q: Let a= and b= Show that there are scalars s and t so that sa+tb=. s = ? t = ?

A: a=-5,0,-3 and b=4,0,2sa+tb=27,0,15

Q: Need help with orthogonal vectors.

A: Step 1: Step 2: Step 3: Step 4:

Q: Select the option that gives the vector product of i+k and i + j Select one: 01 Oi+j-k Oi-j-k…

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Q: 2. In each question, explain the reason. Consider the following vectors in R³: (a) (b) v₁ = (1, 0,…

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Q: Determine the basis that generates the following vector space by clearing the variable y: M = {(x,…

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Q: The vectors v' 1 = (4,5,3), v 2 = (8, r, 6) and v’ 3 = (6,7,8) form a basis of R for any real value…

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Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

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Q: Let F = sin(4x +3z) i-6ye*z k. Calculate div (F) and curl (F). (Express numbers in exact form. Use…

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Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector 8x³ + 2x²7x - 9…

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Q: Find the coordinate vector of a = [*]B= -10-30- 2 with respect to the basis B = for R³.

A: Given: It is given that, x→=42-4 and B=152, 01-6, 001. To find: We have to find the coordinate…

Q: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

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Q: Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.)…

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: 2 A : 10 %3| 0 -1 4

A: To find out solution of homogeneous set of linear equation of A's we have to find the solution of…

Q: The vectors B= = [x]B= = -{].M]} 8 form a basis. Find a vector x given the B-coordinates of x are

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