1. Mar 28, 2014

negation

1. The problem statement, all variables and given/known data

Find the standard matrix of the following linear transformation:

T(x1, x2, x3, x4) = (-2 x1 - 5 x2 - 4 x3 - x4, 2 x1 + 2 x2 - 5 x3 + x4)

3. The attempt at a solution

[x1,x2,x3,x4] [-2,2;-5,2;-4,-5;-1,1]
=[-2 x1 - 5 x2 - 4 x3 - x4, 2 x1 + 2 x2 - 5 x3 + x4]

T(e1) = (-2,2)
T(e2) = (-5,2)
T(e3) = (-4,-5)
T(e4) = (-1,1)

A = [-2,-5,-4,-1; 2,2,-5,1]

The answer has been checked to be correct. But I'm not seeing why the standard matrix has to be transposed?

2. Mar 28, 2014

LCKurtz

A matrix representing a transformation from $R^4 \to R^2$ would be a 2x4 matrix. The images of the basis vectors give the columns. Nothing is transposed that I see.

Last edited: Mar 28, 2014
3. Mar 28, 2014

Staff: Mentor

There are two problems with the above:
1. You have your x vector on the wrong side of A (it should be Ax rather than xA), and your matrix is wrong. You have four rows with two columns - it should be two rows with four columns.
The vectors on the right are all column vectors.
The transformation is T: R4 → R2, so the matrix for T will by 2 X 4 (i.e., two rows with four columns each).

4. Mar 29, 2014

negation

Both of you guys are correct.