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a) Determine whether or not the set of vectors is a basis of the indicated space: x²-1, x*+x+1,x),P; b) Find a basis, and the dimension, of the vector space of all matrices of order 3. c) Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1, 1), (0, 0, -1, 0), (-1, 1, -1, 0) of R'.

a) Determine whether or not the set of vectors is a basis of the indicated space: x²-1, x*+x+1,x),P; b) Find a basis, and the dimension, of the vector space of all matrices of order 3. c) Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1, 1), (0, 0, -1, 0), (-1, 1, -1, 0) of R'.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 2: a) Determine whether or not the set of vectors is a basis of the indicated space: x²–1,x*+x+1,x²,P; b) Find a basis, and the dimension, of the vector space of all matrices of order 3. c) Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1, 1), (0, 0, -1, 0), (-1, 1, -1, 0) of R'.
Transcribed Image Text:Problem 2: a) Determine whether or not the set of vectors is a basis of the indicated space: x²–1,x*+x+1,x²,P; b) Find a basis, and the dimension, of the vector space of all matrices of order 3. c) Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1, 1), (0, 0, -1, 0), (-1, 1, -1, 0) of R'.
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