- #1

Luscinia

- 17

- 0

## Homework Statement

(All matrices are 2x2. Sorry for the awkward formatting)

Find Matrix A such that

(1 -1)

^{-1}(2 3)

(0 1 ) = (1 2) A

^{T}

## Homework Equations

A

_{1}A

_{2}...A

_{k}=A

_{k}

^{-1}...A

_{2}

^{-1}A

_{1}

^{-1}

## The Attempt at a Solution

(1 -1)

^{-1}(2 3)

(0 1 ) = (1 2) A

^{T}

(1 -1)

^{-1}(2 3)

^{-1}

(0 1 ) (1 2) = A

^{T}

((2 3)(1 -1))

^{-1}

((1 2)(0 1)) = A

^{T}

(2 1)

^{-1}

(1 1) =A

^{T}

(2 1|1 0) R1-R2 (1 0|1 -1) (1 0|1 -1)

(1 1|0 1) = (1 1|0 1) R2-R1 = (0 1|-1 2)

A

^{T}=(1 -1)

___(-1 2)

A=(1 -1)

__(-1 2)

The answer was supposed to be (2 -1)

___________________________ (-1 1)