The second column of the matrix of change basis from the basis B = {u= (1,1,1); v = (1,0,1); w= (0,1,1)} to the basis B'= {r=(3,4,1); s=(3,0,1); /= (1,2,0) } is: (3) 0 OA (4 1 B 1 О в. OC/ 2 1 (3) 0 OD. 1 :) OE. 3

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

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Q: Find a basis for R³ relative to which the matrix for T is diagonal, where T(x₁, x2, x3) = (4x₁ + x3,…

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Q: Write x as the sum of two vectors, one in Span fu1,u2,uz} and one in Span fu4}. Assume that fu, .u4}…

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Q: B) Suppose A is an invertible matrix inM, (R). And x, y E R". Prove it: det(A+ ry") = (1+y"…

A: Given: A is an invertible matrix in Mn(ℝ) x,y∈ℝn To prove: det(A+xyT)=(I+yTA-1x)det(A)

Q: Find T(v) by using the standard matrix and the matrix relative to B and B'. T: R2 - R2, T(x, y) =…

A: We have to Find T(v) by using the standard matrix and the matrix relative to B and B.   Given…

Q: 21.1f A' = 34² where A is n by n matrix, then (a) A= 31 (b) A 31 if rank((A) =n () A" =!1 (d) a and…

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Q: For what value of m, the vector (m,3,1) a  linear combination of e\index{1}=(3,2,1) and…

A: We have to find the value of 'm' such that  is a linear combination of Assume

Q: ) If the matrix A= [4 2 1; 1 5 9; 3 8 7], find: · A' - A(3,1) - size(A) - A(:,2)= [] Inv(A)

A: Since, you have posted a question with multiple sub-parts, as per company policy we will solve first…

Q: Given vectors u = (5,0,0), v = (-2,-1,0), and w = (3,7,2), %3D %3D a) Determine if the vectors u, v,…

A: a) u=5,0,0,v=-2,-1,0,w=3,7,2     write it as…

Q: y Suppose E (A, B) is controllable. Suppose a change of basis is performed so that we obtain a new…

A: As per the question we are given a controllable system as : ∑ ➞ (A, B) And after a change of…

Q: Consider matrix attatched and vectors attatched, Let w = Ax+y. Write down w2.

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Q: B = {(1, 2, 4), (–1, 2, 0), (2, 4, 0)}, B' = {(0, 2, 1), (–2, 1, 0), (1, 1, 1)} %3D Find the…

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Q: Find all values of a for which the given vectors form basis for R' a? u = V = and w = a 1 2

A: given vectors u=a201 , v=0a2  and w=101 claim- find all the values of a for which the given vectors…

Q: A' is a 1X3 matrix. The least square solution to the equation A'x=28 is the vector x* =[1 2 3]'…

A: Given that, A' is a 1×3 matrix. A'x=28 ,x*=1 2 3'

Q: 1) Determine whether the given vectors are linearly dependent or linearly independent. a)…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) - (-5x + y, 5x - y), B'- ((1,…

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Q: Ui3(12,7,3.2) u2=( 13.5.3:3) uz= 14=(1,4,697) us%=15,13,13,25, 19) Find a basis of w? consisting of…

A: Full and detailed solution is given below. Dim(w) is number of elements in basis(w)

Q: Find the vector x determined by the given coordinate vector [x] and the given basis B. 8= 6 -6 X =…

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Q: 4) Let V = M2x2 (C) with standard basis B = (m₁, m2, m3, m4) and let T : V → (a) (b) (c) T((& $)) =…

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Q: Given v_(1)=([2],[6]),v_(2)=([1],[4]),S=([4,1],[2,1]) find vectors u_(1) and u_(2) so that S will be…

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Q: 3) Let C be a basis that contains vectors (−2 + 1x + 1x2 + (−1) x3), (1 + (−2) x + 4x2 + 2x3), (−2 +…

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Q: if the chractrestic polynomial of a matrix A is p(^) = (^ +1)(^ - 2)2 then det(-A) +tr (A) = 1 7 -2…

A: As we have 3 roots of characteristics polynomial.

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

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Q: Let T: R³ → R² be defined by T -~--~--E) ----B]}~~(~-| ||-~ ~[]) Let B = u₁ U3 = { = [3], , = 6 (ED)…

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Q: Find the coordinate matrix of X relative to the standard basis for M3,1- X = 11 0 STIFT

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Q: Find change of basis matrix from ((1,2), (3,5)) to ((2,5), (3,7))

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Q: If the matrix A= [2 5 1;7 3 6;2 5 4], find: A' A(2,3) size(A) LA(:,2)=[] Inv(A)

A: We can solve this as follows: