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

Q: Find a basis for the space of 2 × 2 lower triangular matrices. Basis =

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Q: prove that the eigen values of unitary matrix are unit modulus

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Q: If A = {v1, v2, ..., vn} be a basis for FV and n ≥ 2 then, is B = {v1+v2, , v2+v3, ..., vn+v1} also…

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Q: How are n, rank A, and nullity A related to each other how can one find a basis for Col A, Nul A,…

A: Write the relationship between n, rank A and nullity A. Also write a procedure to find a basis for…

Q: Demonstrate that these vectors are not linearly independent. Which pairs of vectors, if any, are…

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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: 3. Give an example of an orthonormal set with 4 non-trivial vectors in R5.

A: We have to solve given problem:

Q: Explain why S is not a basis for M22

A: We have t.o show that why S is not Basis for M2,2: Concept: The dimension of a vector space V, is…

Q: Write standard Basis of P4(x)?

A: P4(x) is a collection of polynomial degree atmost 4

Q: Show that the set S = {1,-1), (1,1)} form a basis for R? Support your answer with an explanation or…

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Q: Let 1 -5 -4 A = 1 1 -1 -3 -5 Find an orthonormal basis of the column space of A. }

A: Solution:- It is given that          A=1-5-411-1-3-52

Q: Find a basis for the nullspace of the matrx. (If there is no basis, enter NONE in any single cell.)

A: Follow the procedure given below.

Q: Let B= { }].[),A} be basis for IR Is B orthonormal ? O False O True

A: Applying orthonormal property we have

Q: Find a basis for the nullspace of the matrix. (If there Is no basis, enter NONE In any single cell.)…

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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: Basis =

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Q: Write standard Basis of P4(x)?

A: Given vector space is P4x

Q: 6) Extend the set S = {(3 ,1,-3)} to a basis for IR³. %3D

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Q: Let B= { be basis for IR Is B orthonormal ?

A: Given B=3-30,22-1,114 be the given basis for ℝ3.

Q: What are two linearly independent eigenvectors of A. Are those eigenvectors linearly independent?…

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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 for S. (Enter sqrt(n) for Vn.) 3 S = span 4 1 6

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Q: Linear Algebra

A: According to the given information, it is required to construct an orthonormal basis of the set:

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: Use Gram Shmidt Algorithm to build an orthonormal basis beginning from the given basis in R: (1, 1,…

A: First part: We have to find the orthonormal basis of the basis 1,1,1,-2,2,1,1,2,2 using the Gram…

Q: [2 Is the collection of matrices a linearly independent set in M2x2? If so, does the collection…

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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: 2. Apply Gram-Schmidt orthonormalisation process to transfom SISBO OUL B= ((4,-3,0), (1,2,0),…

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Q: Assume that {|a), [b), |c)} forms an orthonormal basis in C3 and I4) =la) – i b) +lc) is given. | 15…

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Q: snip

A: Let S=0101,1101 As the dimension of M22 is 4. Also, it has 4 elements, and so it is linearly…

Q: Question. 5 -000 Consider the set x = orthonormal basis for R³. that is a basis for R³. Use the X to…

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Q: Let B= { [}].9Y be basis for IR. Is B orthonormal ?

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Q: Every vector in a space is orthogonal to the zero vector of that space. Every orthonormal basis is…

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

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: ind a basis for the nullspace of the matr

A: Given,         A=13-2501-12-2-64-10

Q: (a) Use the Gram-Schmidt process on the basis {(1,–2, 2), (1, 3, 2), (4, 3, 1)} for R. to find an…

A: Gram- Scmidth Process allow to find orthonormal vector from any basis vector.

Q: Explain why S is not a basis for M2,2.

A: We have given a set of the matrices;

Q: 21 -3 be basis for IR? %3D Is B orthonormal ?

A: check the the determinant of the vectors zero or not. And check the vectors are unit vecors or not

Q: Explain whether S = {(1,0,0), (0,2,0), (–4,0,1), (0,5,0)} is a basis for R³ or not.

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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: 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: ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated…

A: Given  A = 3006-306-63 Its eigen values are -3,3. -3 is the smallest eigen value. The second eigen…

Q: 1. Apply the Gram-Schmidt orthonormalization process to the basis for R² shown below: B = {(3,1),…

A: We will find out the required orthonormal basis.

Q: 3. orthonormal basis B generated by B.

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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)

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

A: Find the Null(A)

Q: be basis for IR? Is B orthonormal ?

A: We have to check whether B is orthonormal or not. Orthonormal means that each pair of vectors must…