Homework for Thursday 10-27 is to read pages 57-60 in the textbook and to show your notes from today, Properties of matrix multiplication and the determinant.
Matrix addition is commutative.
Matrix subtraction is not commutative.
The identity element for matrix addition is a matrix of the same dimension with every entry = 0.
Matrix multiplication is not commutative; A*B does not equal B*A. Changing the order of the two matrices changes the resulting matrix.
For a square matrix, the identity element for mutiplication is a square matrix of the same dimension with 1's on the diagonal which goes from upper left to lower right, and 0's for all the other entries.
For a square matrix with dimension 2x2, with the elements arranged a and b in the top row and c and d in the bottom row, the determinant is a*d - b*c. The determinant will be useful in finding the inverse of certain matrices.
A matrix is a very compact way of representing an arrangement of values, relationships, and coefficients. Matrices can be manipulated and transformed using operations similar to the operations for real numbers.
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