10. For a new basis system the two basis vectors are E',E,+E₂+E, E'=E,-E, where E is 1 1 the standard basis system. Derive the components of the matrix A= 1 2 1 in the new basis system. 1 1 4

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Q: The third column of the change of basis matrix from the basis B={u= (1,1,1); v= (1,0,1); w= (0,1,1))…

A: Given the basis             B=u=1, 1, 1, v=1, 0, 1, w=(0, 1, 1), to the basis,            B'=r=(3,…

Q: 10. It is known that matrix A 4x4 has the following eigenvalues: 2, =-2, 2, = 1, z =-1, 24 = 2.…

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Q: 7. v₁ = (0, 0, 1), V2 (0, 0, 1), V₂ = (7, 4, 11), V3 = (5, 3, 13) 8. V₁ = V1 (2, 0, 0, 0), v₂ = (0,…

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Q: 2 + jai a2 +j Suppose A = is a 5– jaz 3 – ja4 Hermitian matrix then a. aj any real number b. aj = 5…

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Q: Find the coordinate matrix of x in R" relative to the basis B'. [x]g' = B' = {(8, 11, 0), (7, 0,…

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Q: If Q = I - auu" where Qis an orthogonal matrix, a > 0, and u E R"X1 real vector, and I is n x n…

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Q: Q Three vectors (u) (v). (w) have been written in matrix form as shown below: 3 -4 1.5 - Show that:…

A: Given uvw = 2333-421.5-21*ijkuvw =2i+3j+3k3i-4j+2k1.5i-2j+k Thus u = 2i+3j+3kv = 3i-4j+2kw =…

Q: Give a basis for the column space of the matrix A using only columns of A in your basis. 006-10 A =…

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Q: (C). -2 Consider the matrix A = and the vector u = Let B = (A – A")² and define vector v = Bu. If v…

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Q: 1. Two matrix vectors a and b are given as a = -0--0 and b Find (alb).

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Q: (1 point) The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are…

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Q: The second column of the matrix of change basis from the basis B={u= (1, 1, 1); v = (1,0,1); w=…

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Q: The second column of the matrix of change basis from the basis B = {u= (1,1,1); v = (1,0,1); w=…

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Q: 3 2 2 1 a) X1= b) Уi%3D| - 3 y2=| 1 X2= 3 X3= 1 4 y3= 1 3 1 N O

A: X=x1,x2,x3 be set of vectors. Let A=x1,x2,x3 and AT=x1x2x3 G=AAT where G is dram matrix. If G is…

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Q: Find the matrix A' for T relative to the basis B'. A' = T: R² R², T(x, y) = (x + y, 3y), B' = {(-4,…

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

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A: (a)It is given that, P is the change of coordinates matrix from to .Also, the values are:So, using…

Q: |a,6,d e а a, b, d E R}. S2x2 b d Do three matrices 1 A1 = 0 1 1 0 A2 = A3 1 0 - 1 | form a basis of…

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Q: (i.) Suppose ū € R¹ and 7 € R™ are non-zero (column) vectors. Show that the nx m matrix uuT has rank…

A: We know, rank of a matrix = row rank of a matrix = column rank of a matrix.

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A: Let A be the m×n matrix A=a11a12…a1na21a22…a2n⋮⋮⋱⋮am1am2…amnm×n that is the transformation matrix…

Q: A symmetric matrix satisfies M= M'. The set of 2 x 2 symmetric matrices S, with standard matrix…

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Q: If the matrix of change of basis form the basis B to the basis B' is A = OA. 2 (²₂) OB.-2 OC (-2) 3…

A: Given that the matrix of change of basis B to the basis B' is A=-32-21, then find the second column…

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Q: 2 8. A polynomial p(x) = R²[x] has the coordinate 3 relative to the ordered basis B {1,1+ x,…

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Q: Find an orthogonal basis for the column space of the following matrix 0 1 1 1 2 -M = 1 0 0 21

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Q: and ß that solve the vector equation: a (²) + ( )= (²²) (21) B 3 28

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Q: Let A be the 100 by 100 matrix whose i, j entry is (−1)²-¹ + 2/-¹. For example, the top left 3 x 3…

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Q: Q.2) For VR2 and B = {(1,2), (3, 4)"}, C = {(7,3), (4,2)"}; consider one vector v = = (1,0) ¹. •…

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Q: tind an orthogonal boasis for the column Space of the matrix. An orthogonall basis for the of -8 4…

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Q: Suppose A is the matrix for T: R3 → R³ relative to the standard basis. Find the diagonal matrix A'…

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