Applied Math 40S February 4, 2009

What does this picture have to do with matrices?

Matrix

http://ca.youtube.com/watch?v=xyAuNHPsq-g

A little warm up ...

A little warm up ...

http://matwww.ee.tut.fi/cgi-bin/matrix-algebra/MatrixAddition

Suppose that you have access to a woodworking shop in the basement of Amos Hall where you make holiday toys for children as an afternoon activity. Lately you have begun to sell your toys at a local shop. You make four different kinds of toys, namely a train (t), an airplane (a), a dragon (d), and a nameplate (n). Each of these can be made very plainly out of pine (p), or with greater detail and ornamentation out of oak (o). Let matrices O, N, and D represent your sales for October, November, and December, as given below.

1. State the dimensions of the matrices O, N, and D.

5. Construct a matrix S that contains entries representing the total number of each item sold during the three months.

4. How many of each item were sold for the entire three month period?

2,43. What does O represent?

2. How many oak trains were made in December?

Crazy Ken’s Campus Bookstore’s inventory of books consists of the following quantities.

Wacky Wally’s College Bookstore’s inventory of books consists of the following quantities.

Hardcover: textbooks—6340; fiction—2220; nonfiction—1790; reference—1980.

Paperback: textbooks—2050; fiction—3100; nonfiction—1720; reference—2710.

Hardcover: textbooks—5280; fiction—1680; nonfiction—2320; reference—1890.

Paperback: textbooks—1940; fiction—2810; nonfiction—1490; reference—2070.

(b) Represent the inventory of Wacky Wally’s College Bookstore as a matrix.

(a) Represent the inventory of Crazy Ken’s Campus Bookstore as a matrix.

(c) Use matrix algebra to determine the total inventory of a new company formed by the merger of Crazy Ken’s Campus Bookstore and Wacky Wally’s College Bookstore.

Matrices and multiplication... this is called "scalar multiplication" or "multiplication by a scalar".

Now you try ...without your calculator

with your calculator

Now put it all together ...

HOMEWORKSolve for x:

Evaluate:

Solve for x:

Solve for x:

Evaluate:

Evaluate: