and Consider the subspaces of V = R¹X3. Find a matrix X EV such that UnW = span{X}. X=[ U = span{[-1 -1 -2],[-4 −1 −9]} Wspan{[4 -2 2],[-2 1 -13]}

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A: Here we will find matrix of linear transformation

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A: Since the question has multiple subparts, as per the company guidelines, we will solve the first…

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A: We shall answer this question in next step

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A: Step 1:   Step 2: Step 3: Step 4:

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Q: 2x₁ + 4x₂x3 = 15 7x₁3x₂ + 3x3 = -4 4x13x28x3 = 19

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Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

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A: The given matrices

Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

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Q: Suppose that the square matrix A is invertible. Show that the inverse of A is unique.

A: See below the explanation

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A: Since, you have posted multiple questions but according to guidelines we will solve first question…

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A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Notations That Represent A Line

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A: The objective of this question is to prove that if two real symmetric matrices A and B are…