- #1

negation

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- 0

## Homework Statement

Find the standard matrix of the following linear transformation:

T(x

_{1}, x

_{2}, x

_{3}, x

_{4}) = (-2 x

_{1}- 5 x

_{2}- 4 x

_{3}- x

_{4}, 2 x

_{1}+ 2 x

_{2}- 5 x

_{3}+ x

_{4})

## The Attempt at a Solution

[x

_{1},x

_{2},x

_{3},x

_{4}] [-2,2;-5,2;-4,-5;-1,1]

=[-2 x

_{1}- 5 x

_{2}- 4 x

_{3}- x

_{4}, 2 x

_{1}+ 2 x

_{2}- 5 x

_{3}+ x

_{4}]

T(e

_{1}) = (-2,2)

T(e

_{2}) = (-5,2)

T(e

_{3}) = (-4,-5)

T(e

_{4}) = (-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?