- #1

TeenieBopper

- 29

- 0

## Homework Statement

A)Determine the elements of the matrix G such that GY = (Y1 +Y2 + Y3, Y3-Y1, 0.5Y1 - 0.5Y3 +2Y2)'

B)Find the unique symmetric matrix A such that Y'AY = Y'GY.

Y=

[2

7

6]

## Homework Equations

## The Attempt at a Solution

I know that Y1=2, Y2=7, and Y3=6. That means the right hand matrix should be

Z=

[15

4

12]

So:

GY=Z

GYY'=ZY'

G=ZY'(YY')^1

Using proc IML in SAS I get something like:

0.3370787 1.1797753 1.011236

0.0898876 0.3146067 0.2696629

0.2696629 0.9438202 0.8089888

However, I was talking to a friend, and he just matched up the coefficients and got

G=

1 1 1

-1 0 1

.5 2 -.5

This also makes sense to me, so I don't understand why our numbers would be so different. Did I do something wrong in my equation above?

For part B, I did the same thing

Y'AY = Y'GY

Y'AYY'=Y'GYY'

Y'AYY'(YY')^-1 = Y'GYY'(YY')^-1

Y'A=Y'G

YY'A=YY'G

(YY')^-1YY'A=YY')^-1YY'G

A=G

However, G is not symmetric (in either case). I'm not sure what else I can do.

Thanks in advance for the help.