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

Q: Find an orthogonal basis for Null C

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Q: 2 Let A = -3 -1 %3D 1 Find an orthonormal basis of the image of A.

A: Consider the matrix: A=22-3-117 Let v1=(2,-3,1) v2=v2-v2.v1v1.v1v1 =(2,-1,7) -…

Q: Let 4= [ -1 1 2 4 -2 2 Find an orthonormal basis of the row space of A.

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Q: Let 9. A = 3 9 4 6. -3 2 -2 Find an orthonormal basis of the kernel of A.

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Q: Let -4 -6 4 6. A = 6. 2 -2 -6 Find an orthonormal basis of the kernel of A.

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Q: 4. A basis for R3 is Use Gram-Schmidt to find an orthogonal basis for the space.

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Q: Calculate the trace of the change of basis matrix from the basis {(G 1 3 -2 -4 В -1 -2 0 0 to the…

A: Solution of given problem is followed by

Q: (2) Find an orthonormal basis of ColA, where 3 -5 1 1 1 1 A = -1 -2 3 -7 8.

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Q: a' Find the value of a for which S forms a basis for R3.

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Q: Find a basis for the null space of matrix A. A = 1 2 Basis is

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Q: Let [1 37 A = 2 4 Find an orthonormal basis of the image of A.

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Q: 1. Find a basis of the null space of the matrix B = -2 -2 -4

A: See the attachment

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: 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: If and B' are bases of a vector space y and -1 P = is the matrix of transition from the base B to…

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

Q: 3 4 If a basis for R3 is B and given [*]B find i in the standard basis. =

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Q: 3) Let C be a basis that contains vectors (1 + (-1) x + 1x² + 1x³), (1 + 2x + 2x² + (−1) x³), (1 +…

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Q: Let Find an orthonormal basis of the column space of A. A = 1 1 -3 0 -2 -3 1

A: Let A=1-301-2-3-116   To Find: An orthonormal basis of the column space of A.

Q: 4 If a basis for R³ is B = and given [x]B find i in the standard basis. to ]+ G2) + [{]+ C] ó X x…

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Q: If b1, b2 form an orthonormal basis for C and x is any vector in C, then O x4- x bị x b2 0 O x+ x bị…

A: We will find out the required value.

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: Please give correct answer

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Q: (b) Let W be the eigenspace of B corresponding to A = 1. Find a basis for W.

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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: 1. Find an orthonormal basis for the column space, col (A), of the matrix A defined by 3 4 -1 1 3

A: According to the given information, it is required to find the orthonormal basis for the column…

Q: |k)} be an orthonormal basis for H") and {1j)} an orthonormal basis for H2).

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Q: Explain why S is not a basis for P,. .2 S = (1 - x, 1 - x², -1 – 8x + 9x²} O s is linearly…

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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: Let A = -1 -9 3

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Q: The vectors 4 form a basis for R if and only if k #

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Q: Let [2 A = 3 4 2 1 -9 2 -6 nd an orthonormal basis of the kernel of A.

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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: 9. Find a basis for the hyperplane a where a-(2, 1, -3).

A: Any two linearly independent vectors which are orthogonal to the given a are forms a orthogonal…

Q: 1 A = 2 1 1 3 Find an orthonormal basis of the image of A.

A: A=-11-211-3 Orthonormal basis of A using the Gram Schmidt process. v1=-1-21, v2=11-3…

Q: Find the change of basis matrix from G to H. - {[::}[::} [} 6 1 25 5 2 3 1 0 1 1 0 0 0 0 G = H = 0 0…

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Q: (c) Find a basis for the row space of A.

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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: 4 El 4 Let Vi V2 3 and V3 = Use the Gram-Schmidt procedure to construct an ordered - 4 orthonormal…

A: Concept introduction: Gram-Schmidt orthogonalization process Let V be a vector space with an inner…

Q: List every possible spin state for a spin- 3/2 particle in the z-basis. Then, apply Jz, J2, J+, and…

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Q: 11. Perform Gram-Schmidt on this basis to find an orthonormal basis for R? (0) 1 3.

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Q: How is the basis {lk} picked?

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Q: Let Find an orthonormal basis of the column space of A. 2 5 3 -5 3 2 us

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Q: Let 1 A = 9 Find an orthonormal basis of the row space of A

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Q: Let -2 1 A = a- -3 4 Find an orthonormal basis of the row space of A.

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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: find basis and the 1) dimension of w ={A ¢ Mnz: A +=0}

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Q: 9. Let i, j denote the standard basis in R2. Find a scalar c if the vector 7i- 2j is perpendicular…

A: Dot product of the two vectors.

Q: |Let -2 1 -3 A 7 -1 Find an orthonormal basis of the row space of A.

A: Use Gram -Schmidt Orthogonalization process to find the orthonormal basis of the row space of A.