Wednesday, February 7, 2007

Multiplying Matricies

In mathematics, a matrix (pl. matricies) is a rectangular table of numbers, generally a table consisting quatities that can be added and multiplied. In today's class, we learned about the 2 kinds of multiplication in matricies. These 2 kinds are:

  • Scalar Multiplication - is multiplying a matrix by a number.

Given a matrix A and a number n (which is 2), the scalar multiplication cA is computed by multiplying the scalar c by every element of A.

For example:


  • Matrix Multiplication - is the multiplication of two matricies where the number of columns of the left matrix is the same as the number of rows of the right matrix. This involves both multiplication and addition.

For example:

2 x 3 2 x 2 2 x 2


If A is 2 x 3 matrix and B is a 2 x 2 matrix, then the resultant matrix C is a 2 x 2 matrix. Why? Look at the dimensions of the 3 matricies. The inner dimensions are the number of rows and columns of matrix A and the outer dimensions, as we can see, are the dimensions of the resultant matrix C. Is this example commutative? Yes, because in this example, the outer dimensions are the same, which means we can multiply the matricies. In our examples in class, the inner dimensions of the matricies should be the same to multiply them.

And the next scribe is... Jennifer

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