Period+8+-+Inverse+of+a+2x2+Matrix


 * How to find the inverse of a 2x2 matrix**


 * Hans and Mark**


 * __Example.__**

(a b) dd (c d) =A If we insert 1, 2, 3, 4 as example numbers into the Matrix, Matrix A becomes**

(1 2) dd (3 4) =A

Steps:
__1. Determinant needs to be found__ D = ad - cb=1X4 - 3X2= -2 __2. Next, swap the spots a and d__.

(d b) d (c a) = A dd

If we plug in the numbers into example matrix A,

(4 2) (3 1) = A dd

d dd d

__3. Then,Change the Signs of spots b and c__

(4 -2)(-3 1) = A dd

__4. Next, Multiply by the inverse of the determinant__

(4 -2) (-3 1) = A dd X (1/d)

__5. Finally, Multiply the inverse of the determinant by every element in the matrix__

(4 -2) (-3 1) = A dd X (-1/2)

After reducing all fractions, the finally answer is:

(-2 1) (3/2 -1/2) = A dd Therefore (-2 1)(3/2 -1/2) = A^-1 dd

Examples: Find the inverse of each matrix 1. (3 4) (-2 7)

2. (4 5) (8 3)

3. (-2.5 -9.25) (3.75 6.15)

4. (-5.93 -6.42) (7.91 -8.45)

Works Cited:

http://www.algebra.com/algebra/homework/Matrices-and-determiminant/inverse-of-2x2-matrix.solver