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Chapter 5: Q9E (page 263)

If u鈬赌is a unit vector in Rnand L=span(u鈬赌), then projL(x鈬赌)=(x鈬赌.u鈬赌)u鈬赌.for all the vectorsx鈬赌inRn.

Short Answer

Expert verified

According to the definition of the orthogonal projection, projL(x鈬赌)=(x鈬赌.u鈬赌)u鈬赌.

Step by step solution

01

Check whether the given statement is a true or false.

The given statement is if u is a unit vector in Rnand L=spanu鈬赌, then projLx鈬赌=x鈬赌.u鈬赌x鈬赌for all vectors x鈬赌inRn.

By the definition of the orthogonal projection, the formula isprojLx鈬赌=x鈬赌.u鈬赌x鈬赌 .

Then the given statement is false.

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