Standard Matrix of Linear Transformation

[renolovexoxo]

Homework Statement

Let T: R3-->R3, defined by T(x)= a x x
Give the standard matrix A of T, and explain why A is skew-symmetric.

Homework Equations

They define u x v as

u x v=(det [u2 u3/ v2 v3], det [u3 u1 /v3 v1], det [u1 u2/ v1 v2])

For any vectors u,v,w in R3, w.(uxv)=D(w,u,v)

Ax.y=x.A^Ty

The Attempt at a Solution

I'm not really sure how to find a standard matrix for this, so I haven't made much progress.

 

[Ray Vickson]

Homework Statement

Let T: R3-->R3, defined by T(x)= a x x
Give the standard matrix A of T, and explain why A is skew-symmetric.

Homework Equations

They define u x v as

u x v=(det [u2 u3/ v2 v3], det [u3 u1 /v3 v1], det [u1 u2/ v1 v2])

For any vectors u,v,w in R3, w.(uxv)=D(w,u,v)

Ax.y=x.A^Ty

The Attempt at a Solution

I'm not really sure how to find a standard matrix for this, so I haven't made much progress.

If $\textbf{y}= \textbf{a} \times \textbf{x},$ write $y_1, y_2 \text{ and } y_3$ in terms of $x_1, x_2 \text{ and } x_3.$

RGV