(a) How do we compute the vector projection of vector on vector using the dot product? Prove the next statement: If w is the vector projection of vector on vector 7, then vectors - and are orthogonal.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) How do we compute the vector projection of vector on vector using the dot
product? Prove the next statement: If is the vector projection of vector on vector
7, then vectors - and are orthogonal.
(b) Give the characterisation for:
i. two parallel lines in R³ using linear dependence.
ii. a line parallel to a plane using the dot product.
(c) i. Give the definition of the rank of a matrix that involves the matrix echelon form.
ii. Prove the statement: A homogeneous system of linear equations AmxnX = 0 has
a nontrivial solution if and only if rang (A) < n.
Transcribed Image Text:(a) How do we compute the vector projection of vector on vector using the dot product? Prove the next statement: If is the vector projection of vector on vector 7, then vectors - and are orthogonal. (b) Give the characterisation for: i. two parallel lines in R³ using linear dependence. ii. a line parallel to a plane using the dot product. (c) i. Give the definition of the rank of a matrix that involves the matrix echelon form. ii. Prove the statement: A homogeneous system of linear equations AmxnX = 0 has a nontrivial solution if and only if rang (A) < n.
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