SOLUTION: Ichiro Suzuki holds the American League record for the most hits in a single baseball season. In 2004, Suzuki had a total of 262 hits for the Seattle Mariners. He hit three fewer t

Algebra ->  Matrices-and-determiminant -> SOLUTION: Ichiro Suzuki holds the American League record for the most hits in a single baseball season. In 2004, Suzuki had a total of 262 hits for the Seattle Mariners. He hit three fewer t      Log On


   

Question 1114780: Ichiro Suzuki holds the American League record for the most hits in a single baseball season. In 2004, Suzuki had a total of 262 hits for the Seattle Mariners. He hit three fewer triples than home runs, and he hit three times as many doubles as home runs. Suzuki also hit 45 times as many singles as triples.
a) Setup 4 equations using the information given, and the following variables:
s = single, d = double, t = triple, h = home run
So far I got this answer, but I might be wrong:
S+D+T=262
-3T+S+D=262
3D+S+T=262
45S+45T+D=262

I am having trouble with the following questions:
b) Convert your equations to an augmented Matrix
c) If we were doing this by hand, in order to have a diagonal matrix in the end (identity matrix), some rows
need to be swapped. Explain which rows you would “swap” and do so. Re-write the new matrix.
d) Now you may use a calculator to solve the system with the Gauss-Jordan method. Write the solution matrix.
e) Lastly, state in words the number of each type of hit Ichiro got in the 2004 season.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


All of the equations, for solving using matrix methods, need to be in the form
aS%2BbD%2BcT%2BdH+=+n

But 262 is the "n" only in the first equation, which is for the total number of hits.

And in that first equation you left out the home runs.

So a good first equation is
S%2BD%2BT%2BH+=+262

It is more difficult to see how to write the other equations.

"...three fewer triples than home runs..."
T+=+H-3

"...three times as many doubles as home runs..."
D+=+3H

"...45 times as many singles as triples..."
S+=+45T

but you need to put each of those in the required form....

That should help get you started. If you need more help with the problem, resubmit it showing how far you have gotten and one of the tutors here will help you along further.