1. (5 points) Use two arbitrary 2-dimensional vectors to verify: If vectors u and v are orthogonal, then ||u||² + ||v||²

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1 5 Points Use Two Arbitrary 2 Dimensional Vectors To Verify If Vectors U And V Are Orthogonal Then U V 1 (111.28 KiB) Viewed 15 times

1. (5 points) Use two arbitrary 2-dimensional vectors to verify: If vectors u and v are orthogonal, then ||u||² + ||v||² = ||u – v||². Here, ||u||² is the length squared of u. 1 0 2. (5 points) Given a list of three vectors, V₁ = 2, V2 = 2 9 V3 = 3 -4 2 0 Show whether this list of three vectors is linearly independent or linearly dependent. Hint: you can form a matrix [v₁ V2 V3], then use the reduced echelon form. It also works if you use the definition of linear (in)dependence. 3. (4 points) If A is a square matrix and (I - A) is nonsingular. Show (prove) that A(I - A) ¹ = (I - A)-¹A.