Let V be the plane with equation 1 + 4x2 + 5x3 = 0 in R³. Find the matrix A of the orthogonal projection onto the line spanned by the vector 7 = 4 with respect to the basis {6].G]} A =

Q: Find the coordinates of the vector v = (7,4) with respect to the basis U₁ = (2, 1) and u₂ = (3,1).

A: The answer is given below:

Q: Let V be the plane with equation ₁ - 3x2 - 4x3 = 0 in R³. Find the matrix A of the 1 orthogonal…

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Q: Write the vector v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

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Q: Find a scalar equation of the plane that contains the points (−1, −3, 1), (1, 0, 3), and (2, 7, 0).

A: We are going to solve

Q: Let B, D be the following two bases of R³: B = D= 0 0 -2 2 a) Find the change of coordinates matrix…

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Q: Let W be the plane with the equation 3x − y + 6z = 0. Find the standard matrix P for the orthogonal…

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Q: The plane passing through the three points A(0, 1,3), B(3,4,3) and C(2,3, –1) can be expressed as a…

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Q: () 1 (b) Find the length of the component of the projection of the vector a = vector 6 = 2 () onto…

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Q: The vectors B= = [x]B= = -{].M]} 8 form a basis. Find a vector x given the B-coordinates of x are

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Q: Find the equation of the plane P spanned by vectors  v = (2,1, 3)  and w = (1,2,-1)  containing the…

A: The given problem is to find the equation of plane P that is spanned by given two vectors and…