Let B={ }].OH} be basis for IR %3D Find [v]o where 6- 563

Q: Let ¤1,..., IN be data in R" with sample covariance C = XXT. Suppose u; is an eigenvector of C…

A: Given information: The information about a random vector, covariance matrix and eigen values is…

Q: (d) Is {v1, 02, T3, 74} a basis for R4? Why?

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Q: -2 Let y = what are the expansion coefficients of y in the basis {vo, V1, V2 , v3 } you found in the…

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Q: 1. For each of the following, use the Gram-Schmidt process to find an orthonormal basis for R(A): a.…

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Q: (6) Explain why the basis of Ker(T) answers the question.

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Q: 1 3 S = 4 9. a basis for R3? Explain why or why not.

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Q: Explain why S i not a basis for P2. S = {1, 4x, -5 + x?, 3x} O sis linearly dependent. O s does not…

A: We have to find out

Q: After applying the Gram-Schmidt Orthonormalization Process to the basis 8. B = we get the basis a B'…

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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: Which of the following statements are true? Select one or more: Oa. The correlation coefficient…

A: Given :  y1 =e1'X ,..yp=ep'X are principal components . Principal Component analysis is used in…

Q: Find non singular matrices Pand Q such that PAQ is normal form 123 1. Ans. p = Q = 0 31 2 0 0 1

A: The given matrix is, A=123312 The given matrix A is of order 2×3, so pre-multiply A by I2 and post…

Q: XI Let 2 Xi - X z+ Xq = oY be a %3D Xu subset of IR4. which one is the basis for W?

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Q: Let y = 2 1 what are the expansion coefficients of y in the basis {vo, V1, v2 , v3 } you found in…

A: In the Previous question, the vectors v(3) that is forms an orthonormal basis in R4, The vector are…

Q: Explain why S is not a basis for P2.S = {1 − x, 1 − x2, −1 − 2x + 3x2}

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

A: Applying orthonormal property we have

Q: Explain why S is not a basis for R3.S = {(0, 0, 0), (1, 0, 0), (0, 1, 0)}

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Q: find the matna X for T elative to the basis B: T:R'R*, TG j) = (x-J,y-ta), 8'-{(1, -), CO 3)} I D

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Q: Let P = A(ATA)−1AT, where A is an m × n matrixof rank n. Show that P is symmetric.

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Q: How many matrices are there in the vector space Mm×n(Z2)?

A: Here, Z2 has two elements 1 and 0.

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: Explain why S is not a basis for M2,2" 0 1] 1 0 0 1 1 0 O sis linearly dependent. O s does not span…

A: Here given set as S=0101, 1010 Now a, b lies in the field…

Q: After applying the Gram-Schmidt Orthonormalization Process to the basis B={)()} Find the value of a.…

A: By applying Gram-Schmidt Orthogonalization Process we will first obtain a orthogonal basis of the…

Q: b) Find a basis for W. c) What is the dim(W)?

A: You want solution for part B and c, So I have given only part B and c. Basis (definition) Subset B…

Q: Find a basis for Col B where [1 1 0 -2 0 0]

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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: (b) Calculate a basis C for S and state dim(S).

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Q: Explain why S is not a basis for R2.S = {(1, 2), (1, 0), (0, 1)}

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Q: Let A ∈ Mn×n(R) be the matrix defined by Aij= 1 for all i and j. Find the characteristic polynomial…

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Q: Prove that the matrix below is orthogonal for any value of θ.

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Q: and ŷ = Find the values of y, and y, such that vectors = constitute an orthonorma L0.8337! basis in…

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Q: Let }].,)} 3 B = { 1.E be basis for IR %3D 2 Is B orthonormal ? False True

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

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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: Given that f is a polynomial of degree n in Pn, show that { f, f', f'', . . . , f(n)} is a basis for…

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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: QUESTION # 03 Let R have the standard inner product and use the Gram-Schmidt process to transform…

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Q: What is [p]B, the coordinates of p = 4+ 7x with respect to the standard basis B = {1, x} of P1? Ex:…

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Q: Let B = {uj = ,U2 = and C = V2 = Find Pg, the transition matrix from the standard basis of R? to the…

A: Given  B =  u1=21 , u2=11  We have to find PB , the transition matrix from the standard basis of ℝ2…

Q: 1.Assume (f,g) = | f(x)g(x)dx is the inner product for V = P, . Apply the Gram-Schmidt process to…

A: Orthonormal basis

Q: Find the transition matrix from the ordered basis of 3 R? to the ordered basis of R?.

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Q: Q4:Extend the set S={v=(1,0, 1), v2=(1, –1, 1)} to give an orthonormal basis for V3(R).

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Q: Find a 3 x 3 matrix A (with real number entries) whose characteristic polynomial is det(A – rls): *…

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Q: How is the basis {lk} picked?

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Q: Explain why S is not a basis for P. S = {1, 2x, =7 + x², 9x} O S is linearly dependent.

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Q: Show that the condition number of the square matrix, X (generated with X;j = 461-2), grows i+6j–2 as…

A: We will use the conventional definition of condition number of a matrix.

Q: Find the value of Blank-1 Basis Cij 5.58X1 4.5X2 5.36X3 S1 52 аз RHS X3 5.36 -0.125 -0.125 -0.75…

A: The objective is to fill the value of Blank -1 The table is given as,

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…

Q: Given the basis B = { (2, 2) , (0, 2) } for R2. Using Gram-Schmidt, the corresponding orthonormal…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.