Find the 2 x 2 matrix P such that Pu is the orthogonal projection of in R² onto the line consisting of all 3 [³]. 1 scalar multiples of the vector

Q: Find the matrix A of the orthogonal projection onto the line L in R² that consists of all scalar…

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Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: What is the scalar projection of vector a given by (a₁,a2,a3) in the direction of vector b given by…

A: We have to find the scalar projection of a in the direction of b.

Q: state a vector with all non-zero entries which is orthogonal to v⃗

A: Given v vector  Let w vector be orthogonal to v vector  Then w vector . v vector = 0

Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: Find the length of the projection of 3   onto the vector -3…

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Q: Find a vector perpendicular to (2, −1, 10) and (1, 2, −1)

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Q: -9 -10 12 -15 A = 4 -8 6 6 0 9

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Q: 1-5 52 0-4 0 100 -7 0 0 10 -8 0 0 0 0 0 +X5 (Type an integer or fraction for each matrix element.)

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Q: 4. Find representation of the vector v = 2 – 2x+ 6x? with respect to following basis. {1+ 3x + 3x?;…

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Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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Q: Use matrix multiplication to find the orthogonal projection of (-8, 5, 7) on the xy-plane. Let T…

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Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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Q: Make the vectors u1=(2,0,-1,1), u2=(1,1,-1,3), u3= (-1,1,1,-1) orthonormal.

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Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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