INTRODUCTION TO MATRICES MATRIX ABOUT MATRICES A MATRIX

INTRODUCTION TO MATRICES (MATRIX)

ABOUT MATRICES § A MATRIX IS A RECTANGULAR ARRANGEMENT OF NUMBERS IN ROWS AND COLUMNS. ROWS RUN HORIZONTALLY AND COLUMNS RUN VERTICALLY. § THE DIMENSIONS, OR SIZE, OF A MATRIX ARE: # OF ROWS X # OF COLUMNS.

ARRANGING A CLASSROOM Row 1 Row 2 Row 3

ARRANGING A CLASSROOM Row 1 Row 2 Row 3 Column 1 Column 2 Column 3 Column 4 Column 5

ARRANGING A CLASSROOM Row 1 Row 2 Row 3 Column 1 Column 2 Column 3 Column 4 Column 5

3 – Rows 5 -- Columns Dimension of the Classroom ---- 3× 5 Matrix

MATRIX • RECTANGULAR ARRAY OF ELEMENTS 3 by 4 Matrix 3 ---- Rows 4 ---- Columns

Dimension of a Matrix (Row×Column) MANGO ORANGE GRAPE RAHIM 3 5 0 KARIM 0 8 1 RAFIQ 3 0 1 3 × 3 MATRI X

SPECIAL MATRICES SOME MATRICES HAVE SPECIAL NAMES BECAUSE OF WHAT THEY LOOK LIKE. a) ROW MATRIX: ONLY HAS 1 ROW. b) COLUMN MATRIX: ONLY HAS 1 COLUMN. c) SQUARE MATRIX: HAS THE SAME NUMBER OF ROWS AND COLUMNS. d) ZERO MATRIX: CONTAINS ALL ZEROS.

IDENTITY MATRICES § AN IDENTITY MATRIX IS A SQUARE MATRIX THAT HAS 1’S ALONG THE MAIN DIAGONAL AND 0’S EVERYWHERE ELSE. § WHEN YOU MULTIPLY A MATRIX BY THE IDENTITY MATRIX, YOU GET THE ORIGINAL MATRIX.

FIND THE DIMENSIONS OF EACH MATRIX. DIMENSIONS: 3 X 2 DIMENSIONS: 4 X 1 COLUMN MATRIX DIMENSIONS: 2 X 4

ADDITION AND SUBTRACTION OF MATRICES • TWO MATRICES CAN ONLY BE ADDED OR SUBTRACTED IF THEY HAVE THE SAME DIMENSIONS. • THE CORRESPONDING ELEMENTS OF THE TWO MATRICES ARE EITHER ADDED OR SUBTRACTED.

EXAMPLE: ADDING MATRICES EXAMPLE: FIND A + B. SOLUTION: A+B

PRACTICE PROBLEM: DETERMINE A-B

SCALAR MULTIPLICATION • A MATRIX MAY BE MULTIPLIED BY A REAL NUMBER, A SCALAR, BY MULTIPLYING EACH ENTRY IN THE MATRIX BY THE REAL NUMBER. DETERMINE 3 A