Thread: PLEASE HELP! (Matrix problem!)

Hey everyone, I feel pretty ridiculous for asking help with a simple(?) problem, but it's been too long since I've worked with matrices and to be honest, I'm stumped. That and the way it's worded...

Here it is:

Bob is making a mobile. He wants to suspend three objects from a lightweight rod, as shown. Suppose the weighs of the objects are w1= 2.5 oz, w2, 1.2 oz, and w3, 2.0 oz.

a. Write three equations involving the unknown distances, d1, d2, and d3 based on the following facts:
- The length of the rod is 14.5 in.
- To balance the mobile, he must position the objects so that w1d1= w2d2 + w3d3.
- He wants the third object to be 1.5 times as far from the support as the second object is.

The only equation I'm sure of is d1 + d2 + d3= 14.5
How would I set up an equation for the 2nd fact so I can put it in a matrix equation? Wouldn't it be 2.5d1 = 1.2d2 + 2d3? Since I have to put all the variables on one side, would the other side just be "0"?

b. Write the system of equations as a matrix equation.

This is all I have:
a x b
[ 1 1 1 ] [ d1 ] [ 14.5 ]
[ ] [ d2 ] = [ ]
[ ] [ d3 ] [ ]
Sad, I know.

c. Find d1, d2, and d3.


Ahh, I'm so bad at math. If someone can guide me through this problem, I will be eternally grateful. :')

EDIT: Nevermind, I got it. : P

Originally Posted by miyosuke

...

a. Write three equations involving the unknown distances, d1, d2, and d3 based on the following facts:
- The length of the rod is 14.5 in.
- To balance the mobile, he must position the objects so that w1d1= w2d2 + w3d3.
- He wants the third object to be 1.5 times as far from the support as the second object is.

...

Hello,

only a hint:

you wrote:
- He wants the third object to be 1.5 times as far from the support as the second object is.

According to your sketch that means: