Let W be the subspace spanned by u, and u,. Write y as the sum of a vector in W and a vector orthogonal to W. 13 1 y = u, = 3 14 1 4 ...... O A. 15 OB. 12 - 11 y = 13 y = 10 6. 20 C. 11 O D. 6. y = 10 - 7 y = 20 - 17 10

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

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Q: Y1 Let v = and w = be vectors in R. Compute the following. Y2 Y3 Preview Preview Preview

A: Given the vectors        v→=x1x2x3 and w→=y1y2y3 be vectors in ℝ3. Compute w→-v→.

Q: -2x – 4y + 2°z = 1 ) %3D Solve the following linear system. 3x2 + 2x3 – x4 + 2x5 = a 3x1 -9x2 + 7x3…

A: by backward substitution find values

Q: O a Ob 1. Which of the following is a set of linearly independent vectors? a. (1,2,1),(1,2,2),…

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Q: Are the following vectors linearly independent? Yes No , ,,

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Q: -91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal…

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Q: Write vas the sum of two vector components if v= 2i+jand w=3/- 2j. O-(-+)+(¹+) O )+(¹+)) O (+)+(+) O…

A: Write v as the sum of two vector components if v=2i+j and w=3i-2j.

Q: 13. Write the reduced echelon form of a 3 x 3 matrix A such that the first two columns of A are…

A: 13. Given that A3-21=000. We have to find a 3×3 matrix Athat has first two columns of A are pivot…

Q: Let x 4 || - N and y = Find the vector v = 3x - 4y and its additive inverse. 18 [2] 4

A: The additive inverse of a vector v = <a , b> is  - v = <-a , -b>

Q: find the components of the vector −→P Q. P = (1, 0, 1), Q = (2, 1, 0)

A: Given  P=<1,0,1>Q=<2,1,0> The component form of a vector is the ordered pair that…

Q: Find the closest point to y in the subspace W spanned by v₁ and v2. y= 3 -1 1 16 V1 11 1 -4 1 5 V2 =…

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Q: 0-0-0 2. 11 S = { %3D linearly dependent or linearly independent?

A: A set of vectors {v1, v2......vn} is said to be linearly independent if there exist scalars, such…

Q: -0-0-0-0 3 and b (a) Determine if bis a linear combination of a,, a, and a,. (b) Determine if the…

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Q: Determine which of the following sets of vectors are linearly independent and which are linearly…

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Q: Find the dimension of the subspace spanned by the given vectors below. 4 6. -5 8 -4 O 3 O 4

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Q: Is the following set of vectors linearly independent? {·O·} 2 0 5 6

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Q: Let y = #₁ = 1 and = 2 -27 -2 Write y as the sum of two orthogonal vectors, 1 in Span{u} and 2…

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Q: . The distance of a point in the 3-D system from the origin a. is defined by the absolute value of…

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Let x = (2, 5, 1) and y = (−1, 3, 2) be two vectors in R3. Compute xTy. Compute xyT. Are x and y…

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Q: Which of the following vectors is a linear combination v1 v2 and v3?

A: this is a problem of linear transformation.

Q: -0-0--0--0--0- 1 19. Let S be a set of vectors such that u = whether the set of vectors is linearly…

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Q: 2. Check whether each of the following sets of vectors is linearly independent, and determine the…

A: We can conclude the independency by finding the determinant of {u,v,w}. if the determinant of the…

Q: Q1. Construct an orthogonal set of vectors from the following vectors: X1 = k,X2 ,X3 %3D 14]

A: Use the usual inner product in the vectors and Gramm-smidth orthogonalisation process.

Q: 7. u = (2, 2), v = (2, −2) 8. u = (2,-2), v = (−2, 2)

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Q: 5. v₁ = (1, 0, 0), V₂ = (0, -2, 0), V3 = (0, 0, 3)

A: The given vectors are as follows:To Find:whether the given vectors u and v are linearly dependent or…

Q: 1 1 1 V1 = 1 V2 x = 3 4 et V = span{v1, v2}. 1. Find V+. In other words, find u̟ and uz such that V-…

A: First find Vperp and the find X and Y