QUESTION 1 Let A = [ 0 1 -1 0 W₁ and B = 0 [69]." It is given that = {X € M₂x2 (C): AX = XB} and W₂ = {X € M₂x2 (C) : AX are subspaces of M₂x2 (C). (1.1) Find a basis for W₁. (1.2) Find a basis for W₁n W₂. (1.3) Explain whether M₂x2 (C) = W₁ W₂. =iX} =

Q: 1 -2 4 5 If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine…

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A: It can be verified that Using this information we have to find a basis for H.

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A: we will find the required.

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A: Here given A=1-2301-44-912, b=-6-15-5 Here given linear transformation as Tx=Ax

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Q: Define T:R-→R² by T(x) = Ax. Find a basis B for R² with the property that [T]B is diagonal. - 3 - 3…

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

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Q: 3. Consider the vectors 1 W1 E W2 = and the subspace W = span{w₁, W2, W3} CR¹. (a) Find an…

A: Given, as a matrix: 10-1121011000    ~       10-1022000000   Rank = number of pivot elements =2w1,…

Q: 3. Suppose that {v1, v2, V3} is a basis for V and p:(v;) = dij. Let %3D W1 = 2v1 + v2, W2 = v1 -…

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A: Answer and explanation is given below..