20. (1) Give the coordinates of (4, 1, 5) in the basis (:) () ) (2) * Give the coordinates in the canonical basis of the point whose coordinates in the basis above are (3,2,6) (3) Give the coordinates of (10, 3, 6) in the basis (:) () ) 3 2

Q: 2, Xz} is a basis of V, (R). show that {, +X, X2 + X3, X3 +Xi} is also a basis of V, (R),

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Q: 7) Is the basis B = an orthonormal basis? If it's not, then can we make it to become one?

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Q: the coordinates of (2, 3, 4, – 1) with B = {(1, 1, 1, 2), (1, –1, 0, 0), (0, 0, 1, 1), (0, 1, 0, Q}}…

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Q: 4. Prove that ū = (1,0, 1), ở = (2, 2, –1) and w = (-2,3,0) are a basis for R. Use these three…

A: Given u=(1, 0,1), v=(2, 2,-1), w=(-2, 3,0)  To check they form a basis for R3 or not.

Q: 14. a) Use the Gram Schmidt Orthogonalization Procedure to transform the basis {(0, 1, 2), (1, 1,…

A: The given basis of for R3 is 0,1,2, 1,1,2, 1,0,1

Q: Let 1 1 -4 A = -3 9 -6 -2 8 -7 Find an orthonormal basis of the column space of A. 4 -18/5 -6 36/5

A: Consider the matrix A=[11-4-39-6-28-7]We find the basis for the…

Q: 2. Find the matrix of the linear transform æ → Ax = (x1-82 + x3, x1 – #2, x2 – 23), x = (x1, #2, 13)…

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Q: If a, b, c are given with a -/=- 0, how would you choose d so that [ � �] has rank 1? Find a basis…

A: To have rank 1, given that the first row is non-zero, the second row should be a multiple of the…

Q: Let A = 3.6 1 -8 Find an orthonormal basis of the image of A.

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Q: Find the coordinate matrix of x = (−2, 1, 3) in R3 relative to the standard basis S = {(1, 0, 0),…

A: Given: Then,

Q: 14. Find the standard matrix that performs the clockwise rotation of vectors in R² about the origin…

A: A linear transformation is a mapping that connects a vector space to another vector space. Every…

Q: Suppose that in solving an LP, we obtain the tableau in Table 22. Although x1 can enter the basis,…

A: We know that, if in an LPP if all the elements of any column are less than or equal to zero then the…

Q: 1. Construct a 3D orthonormal basis, where the first basis vector is along (3, 4, 0), the second is…

A: We need to calculate an orthonormal basis.  We are given a vector and an axis perpendicular to it.

Q: 2 Find an orthogonal basis for the space spanned by 4 and

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Q: 1. Show that the vectors (1, 1,0), (1, 1, 1) and (1,0, 0) are a basis of R3. Find the coefficients…

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Q: 8. Prove that ū = (2,2, 1), ī = (-1,0,1) and w = (-2,3,0) are a basis for R³. Use these three…

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Q: Show that the vectors (1, 1, 2), (1,2,5), (5,3,4) of R'(R do not form a basis of R'(R).

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Q: 4. A = 3 -6 -12 -3 -6 -9 -3 Find an orthonormal basis of the kernel of A.

A: Note: We know that the kernel of a matrix A is the set of solutions of the corresponding homogeneous…

Q: 3) li) Find the dual basis {l, l} of the standard basis of IR". (i) Fiod th

A: Since you have asked more than one question, we will solve first one for you. If you want other…

Q: 5. Use the fact that {eina} is an orthonormal basis for L2(-7, T) to deduce that {cos(nx)} {sin(nx)}…

A: Consider the equation

Q: Find an orthonormal basis of the plane x1 + 8x2 – x3 = 0.

A: That's easy. Have a great day!!!

Q: 1 3 1 -1 2 0 5 -2 6 1 A = 3 -1 3 4 1 -3 -2 3

A: We have to find the Nul(A).

Q: Suppose that a₁,a2,..., a, form a basis of R" and y = ₁²₁ +2₂₂ + ... + n Anan with 2; = 0. Prove…

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Q: 2 1 Find an orthogonal basis for the column space of A = -1 -1

A: INTRODUCTION: If every pair of different vectors in a set is orthogonal, the set is termed an…

Q: Find an orthogonal and an orthonormal basis for 5 1 2 W = Span Spa { ·} 0 2 -2 -4 0

A: GRAM-SCHMIDT METHOD The Gram-Schmidt process (or procedure) is a sequence of operations that allow…

Q: (0,0, 1), (0, 1, -1)} be a basis of R, Find the matrix for T relative to

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Q: 4 コ 2 %3D 1

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Q: Verify that {(sin θ, cos θ), (cos θ, −sin θ)} is an orthonormal basis for R2.

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Q: 3. Find a basis among the vectors [1, 2, 3], [2, 6, 10], [0, –3, –6],[-1,-3,-5] (which are surely…

A: Q3 asked and answered.

Q: Prove that the vectors (1, 1, 0),(1, 2, 3) and (2, −1, 5) form a basis for R3

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Q: 3. In the space of square matrix M2x2 find representation of vector A = L4 from the basis U1 ; Uz =

A: As basis is given . So, vector A can be written as linear combination of basis vectors .

Q: -2 5 -3 1 1 2. Let S = 5 -1 7 Find an orthonormal basis for the space spanned by the -3 -2 -10 -1…

A: Given matrix is: S=-25-3110-175-3-2055-10-1

Q: Find an orthonormal basis of the plane x1 - 6x2 - x3 = 0. { }

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Q: If B = {(1,1,0), (0,1,1), (-1,0,2)} is a basis of R³, then the coordinate vector of v = (2,0,1) in…

A: Solve the following

Q: find the change-of-coordinates matrix from the basis B = In P2. : {1- 2t + t²,4 – 7t + 5t,5- 8t +…

A: Let's find.

Q: Here ê, are orthonormal unit base vectors in R³. 2.12 Let the vectors (i, j, k) constitute an…

A: Given: Vectors are  e1=-i^-j^e2=i^+2j^-2k^e3=2i^+j^+k^ To find: (a) the dual or reciprocal…

Q: Find a basis for R which contains as many vectors as possible of the following quantity: {(1, 2, 0,…

A: Let us first verify whether the above vectors are linearly independent or not. Thus, the vectors…

Q: Is it {C1,-1, 0,2), (3,-1,2,1)( 18,0,1)3 R Basis ?

A: The objective is to solve the above question.

Q: How is the basis {lk} picked?

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Q: 4 2 If a basis for R3 is B = and if a vector in the standard basis is i = |-4|, find its 5…

A: We know, The set B of vectors in a vector space V is called a basis if every element of V can be…

Q: 9 - - Let 1 3 5 A = -1 5 4 9 2 4 6 10 Which one is a basis for the column space, C(A), of A

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Q: 14.a) Use the Gram Schmidt Orthogonalization Procedure to transform the basis {(0, 1, 2), (1, 1, 2),…

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Q: 5. Determine the coordinate veltor of V =(8,-4,-12) velative to the basis S = {(,,1),(1,5,-3),…

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Q: Let 3 A = 1 2 -8 2 Find an orthonormal basis of the row space of A.

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Q: 3. Do the vectors (1, 1,0), (0, 1, 1) and (1,0, -1) form a basis of R3?

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Q: ´) Consider the vectors - - (-) · · - () ₁ - - () a= 2 Do these vectors form a basis of R³? If yes,…

A: They form a basis for R3. Explanation is as follows

Q: Show that the vectors (1, 1, 2), (1, 2, 5), (5, 3, 4) of R'(R) do not form a basis of R'(R).

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Q: How would you represent it in Basis 2?

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Q: 2 -4 1 -7 1 -2 1 -5 6 -12 3 A = -21

A: Compute the standard basis of Nul(A) for the matrix (No need to show work for calculating rref)