Linear Transformations matrix help

[DanielJackins]

Homework Statement

Two questions;

1. Let v1 = [-3, -4] and v2 = [-2, -3]

Let T: R^2 -> R^2 be the linear transformation satisfying T(v1) = [29, -35] and T(v2) = [22, -26]

Find the image of the arbitrary vector [x, y]

T[x,y] = [ _ , _ ]

2. The cross product of two vectors in R^3 is defined by [a1,a2,a3] x [b1,b2,b3] = [a2b3-a3b2, a3b1-a1b3, a1b2-a2b1]

Let v = [2,6,-4]

Find the matrix A of the linear transformation from R^3 to R^3 given by T(x) = v x x.

A = ? (3x3 matrix)

The Attempt at a Solution

For question 1, I found a T[x,y] but it's a 2x2 matrix [{-197, -8/7},{135,8/7}], but maybe I'm understanding the question wrong?

And for question 2, I really have no idea where to start. Wouldn't I need to be provided with a matrix x if were to find T(x) = v x x? Thanks for any help

 

[LCKurtz]

You are confusing the representation of the transformation as a matrix with its result as an operator. The domain and range of the operator in 1 is R². I didn't check your calculations in 1, but if the transformation is represented by the matrix you say it is, you should be able to calculate T([x,y]), which should be in R².

You got the matrix in part 1 by knowing what T did to a couple of points in R². Do the same thing for part 2.