Find an orthogonal basis of the column space of the following matrix: 2 6 2 4 A = 2 1 4 5 2 4 1 2 2 -3 2 -5 0 -4 0 1

Q: Prove that the column vectors of the matrix B = space of the matrix B. U 2 128 0 4 2 are dependent.…

A: The given matrix .The aim is to prove that the column vectors of  are dependent and describe the…

Q: If A and B are 2 × 2 orthogonal matrices, show AB is also orthogonal.

A: Let A and B be    orthogonal matrices.We have to show that AB is an orthogonal matrix.We know thatA…

Q: Find the following matrix product. Be careful to distinguish 2 x 2 matrices in the answers from 2 x…

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Q: -1 6 3 -8 3 1. Find an orthogonal basis for the column space of the matrix 1 -2 6 1 -4 -3

A: Gram Schmidt Orthogonalization process- Let the orthogonal basis is denoted by, {v1, v2,......} and…

Q: Find the change-of-coordinates matrix from Bto the standard basis in Rn.

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Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

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Q: In P,, find the change-of-coordinates matrix from the basis B = {1-7,2 +t- 13t2,1 + 6t} to the…

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Q: Find a basis for the column space and null space of the matrix 1 -2 0 -2 T = 1 -3 0 -1 -2 0 1 1

A: The given matrix is T=1-20-21-30-1-2011.

Q: List the row vectors and column vectors of the matrix 1. 2 5 7 –10 1 3 1 1 4 2 7

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Q: (3) Find an orthogonal basis of the column space of the matrix -1 6 6 3 6 -4 -3, A= 3-8 1-2 1

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Q: Find the rank of the following matrices: 1 2 2 3 3 2 1 тank(A)— 2 3 таnk(A)—

A: We use the definition of the rank of a matrix to find the rank of given matrices.

Q: Find an orthonormal basis for the column space of 7 -11 1 -4 -1 0 2

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Q: Use the definition of Ax to write the vector equation as a matrix equation -2 + Z2 - 5 3 +Z4 2 4 Z1…

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Q: Find an orthogonal basis for the column space of -1 27 -1 2 -3 0

A: The given matrix is .To find the orthogonal basis for the column space of the matrix.