# Find a formula for T^−1 if

• Feb 24th 2013, 10:41 PM
UBCBOY
Find a formula for T^−1 if
I don't understand how to do this question! Doesn't it just mean to find the inverse of matrix T?

Find a formula for T^-1 if

T(x1,x2) = (8x1 - 4x2, 6x1 - 6x2)

Therefore:

T^-1(x1,x2) = (_x1 + _x2,_x1 + _x2) ?

What's the matrix of T...
Wouldn't it be like:
[8 -4]
[6 -6] ?!

Thank you so much...I'm confused.
• Feb 25th 2013, 07:41 PM
chiro
Re: Find a formula for T^−1 if
Hey UBCBOY.

In terms of the formula, do you know the formula to find the inverse of a 2x2 matrix?
• Feb 27th 2013, 03:25 AM
Deveno
Re: Find a formula for T^−1 if
in general, if we have the matrix

$\displaystyle A = \begin{bmatrix}a&b\\c&d \end{bmatrix}$

and ad - bc is non-zero, then:

$\displaystyle A^{-1} = \frac{1}{ad - bc}\begin{bmatrix}d&-b\\-c&a \end{bmatrix}$.
• Feb 27th 2013, 05:44 AM
HallsofIvy
Re: Find a formula for T^−1 if
Are you required to use matrices? You are given T in terms of equations, not matrices. From "T(x1,x2) = (8x1 - 4x2, 6x1 - 6x2)"
you know that y1= 8x1- 4x2 and y2= 6x1- 6x2. Solve those two equations for x1 and x2 in terms of y1 and y2, then, to get the form you want, swap "x" and "y".