Math Solutions

[Solved] Cross-product. The cross product of two 3 -vectors a=(a_1, a_2, a_3) and x=(x_1, x_2, x_3) is defined as the vector a *

Question: Cross-product. The cross product of two 3 -vectors \(a=\left(a_{1}, a_{2}, a_{3}\right)\) and \(x=\left(x_{1}, x_{2}, x_{3}\right)\) is defined as the vector

\[a \times x=\left[\begin{array}{l} a_{2} x_{3}-a_{3} x_{2} \\ a_{3} x_{1}-a_{1} x_{3} \\ a_{1} x_{2}-a_{2} x_{1} \end{array}\right]\]

The cross product comes up in physics, for example in electricity and magnetism, and in dynamics of mechanical systems like robots or satellites. (You do not need to know this for this exercise.) Assume \(a\) is fixed. Show that the function \(f(x)=a \times x\) is a linear function of \(x\), by giving a matrix \(A\) that satisfies \(f(x)=A x\) for all \(x\).

Price: $2.99
Solution: The downloadable solution consists of 1 pages
Deliverable: Word Document


∴ Other downloads you may be interested in ∴

log in to your account

Forgot password?
Don't have a membership account?
REGISTER

reset password

Back to
log in

sign up

Back to
log in