a. The linear mapping G projects the space vectors orthogonally onto the plane 3x + 2y + z = 0. Determine the mapping matrix of G. b. Let F be a linear mapping from ℝ³ to ℝ³ such that the equation F(x) = x only has the solution x = 0. Prove that the equation F(x) = y + x is solvable for every y in ℝ³.
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One way to do this is to find two linearly independent vectors that lie in the plane. Show more…
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