MA 265 Chapter Revies... Chapter 1 - Chapter 5

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Chapter 1

Matricies

A = [a b c; d e f; g h i] this is a 3x3 Matrix. 3 rows and three colums. The rows are seperated by a semicolen.

B = [a b c d; e f g h] this is a 2x3 Matrix. 2 row and 4 colums. Entry Asub(2,3) = g

- matricies are only equal if each corrisponding entry is the same.

- Matrix Addition = add the values of the corresponding matrix entries.

- Matrix Scalar Multiplication = r[a1 a2; a3 a4] = [ra1 ra2; ra3 ra4]

- Linear Combinations = c1A1 + c2A2 + ... + ckAk where c is a scalar and A is a matrix.

- Transpose Matrix(A^T) = say A = [a1 a2 a3 a4; b1 b2 b3 b4; c1 c2 c3 c4] the A^T = [a1 b1 c1; a2 b2 c2; a3 b3 c3; a4 b4 c4]

     notice that A   is a (3x4) matrix = 3 rows and 4 columns 
                 A^T is a (4X3) matrix ... the rows and the colums interchange.

Back to 2010 Fall MA 265 Momin

- Matrix Multiplication : C = a1ib1j + a2ib2j + .... + aipbip