10-18 Multiplying matrices

Homework for 10-19 or after Career Fair
Page 56; items 16a, 16b, 16c and 1, 2, 3, 4, 5, 6, 7, 8 on the bottom

Page 53 in Springboard, item 10:  The matrix multiplication example takes each person row and multiplies it by each wood column, using all 6 combinations of Monique and Shondra with Walnut, Maple and Cherry.

A 2x3 matrix with 2 rows and 3 columns can multiply a 3x2 matrix with 3 rows and 2 columns.
The result is a 3x3 matrix.
A 2x3 matrix and a 3x2 matrix can be multiplied because the # of columns in the first equals the # of rows in the second (2 = 2).
The result is a 3x3 matrix because that's the # of rows in the first and the # of columns in the second.

A 1x4 matrix with 1 rows and 4 columns can multiply a 4x2 matrix with 4 rows and 2 columns.
The result is a 1x2 matrix.
A 1x4 matrix and a 4x2 matrix can be multiplied because the # of columns in the first equals the # of rows in the second (4 = 4).
The result is a 1x2 matrix because that's the # of rows in the first and the # of columns in the second.

A 2x3 matrix with 2 rows and 3 columns CANNOT multiply a 2x3 matrix with 2 rows and 3 columns.
A 2x3 matrix and a 2x3 matrix CANNOT be multiplied because the # of columns in the first DOES NOT EQUAL the # of rows in the second (3 does not equal 2).
If you try to multiply a row by a column, the number of corresponding entries does not match.