Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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All vectors are in R".
Check the true statements below:
A. If L is a line through 0 and if ŷ is the orthogonal projection of y onto L, then ||ŷ|| gives the distance from y to L.
B. If y is a linear combination of nonzero vectors from an orthogonal set, then the weights in the linear combination can be
computed without row operations on a matrix.
C. A matrix with orthonormal columns is an orthogonal matrix.
D. If the vectors in an orthogonal set of nonzero vectors are normalized, then some of the new vectors may not be orthogonal.
E. Not every linearly independent set in R" is an orthogonal set.
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Transcribed Image Text:All vectors are in R". Check the true statements below: A. If L is a line through 0 and if ŷ is the orthogonal projection of y onto L, then ||ŷ|| gives the distance from y to L. B. If y is a linear combination of nonzero vectors from an orthogonal set, then the weights in the linear combination can be computed without row operations on a matrix. C. A matrix with orthonormal columns is an orthogonal matrix. D. If the vectors in an orthogonal set of nonzero vectors are normalized, then some of the new vectors may not be orthogonal. E. Not every linearly independent set in R" is an orthogonal set.
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