Answer to Question #331640 in Linear Algebra for Athar

Question

In Exercises 15–16, determine whether the expression makes sense mathematically. If not, explain why?

15. (a) u · (v · w)

(b) u · (v + w)

(c) u · v

(d) (u · v) − u 

Answer 1

(a) u · (v · w) - makes sense

vector • (vector • vector)=vector • scalar = vector

Ok.

(b) u · (v + w) - makes sense

vector • (vector + vector)=vector • vector = scalar

Ok.

(c) u · v - makes sense

vector • vector = scalar

(d) (u · v) − u - error

(vector • vector) - vector = scalar - vector

Operation “scalar - vector “ is undefined.