Which of the following sums cannot be simplified?

3-6 Multiplying Matrices Follow the rainbow!

Two matrices can only be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix. For example, the product of Am × n and Bn × t is a matrix with dimensions m × t. In matrix multiplication, the elements of a row in one matrix are multiplied by the elements in a column of the second matrix. Like matrix addition and subtraction, the result of the combination is a single element.

A= 𝑎 𝑏 𝑐 𝑑 B= 𝑒 𝑓 𝑔 ℎ 2 x 2 A·B = 𝑒 𝑓 𝑔 ℎ 𝑎 𝑏 𝑐 𝑑 = 2 x 2

11. Find the product, if possible 2 5 −3 1 3 −1 8 −3 · 6 −3 −7 1 2 0 −1 0

25. Find the product, if possible. −1 0 6 −4 −10 4 · 5 −7 −2 −9

You will need to be able to multiply by hand for the test You will need to be able to multiply by hand for the test. DON’T GET DEPENDENT ON YOUR CALCULATOR! It is a tool, not a crutch. Sung to tune, "My Darling Clementine." Row by column, row by column  Multiply them line by line  Add them up to form a matrix  Now you're doing it just fine!

p. 187 3-6 Graphing Technology Lab To enter matrices on your calculator: Choose 2ND MATRIX (by x-1 button) Hit the right button twice to select EDIT. Choose which name to use. Give the appropriate dimensions, and then enter the matrix, which builds across a row, then pops down to the next row to repeat. Make sure you hit enter after the last element. On your main screen, do the math with the matrices you have entered. Problems 1-5 odd

Notice they do not rearrange the left distributive property so it says AC + BC. Why? Is there a commutative property of matrix multiplication? From the matrices from p. 187, try AB and BA. Are they the same result? Is AB = BA?