Let 7 = A = The cross product of two vectors in R³ is defined by a1 a2 a3 b₁ = xb₂ b3 a₂b3a3b₂ a3b₁a₁b3 La₁b₂a₂b₁. 2 -B 5 . Find the matrix A of the linear transformation from R³ to R³ given by T() = v x x.

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Q: 3) Let A = 2 -1 Find a matrix P that orthogonally diagonalizes A. Use P to com- 0 -1 pute A5.

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Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

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A: The given vectors are  a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k

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Q: Consider the vectors ā₁ = (-1,2,2), a2 = (2,2, -1), and 3 = (2,-1,2). 1. Compute the projection…

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

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A: see below the answers

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A: To find Whether the given vectors are limearly independent or not.

Q: b) Express the vector (–1,5, -6) in R³ as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

A: See the detailed solution below.

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Q: 5. Show that the vectors a = 3i-j+ 4k, b =i-3j–2k and e = 4i– 3j+2k are linearly independent. Find…

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