MATH 105: Finite Mathematics 2-4: Matrix Algebra Prof. Jonathan - PowerPoint PPT Presentation

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion MATH 105: Finite Mathematics 2-4: Matrix Algebra Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Outline The Basics of Matrices 1 Matrix Addition 2 Scalar Multiplication 3 Conclusion 4

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Outline The Basics of Matrices 1 Matrix Addition 2 Scalar Multiplication 3 Conclusion 4

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Exploring a Matrix Since we’ve seen that matrices can be useful in solving equations, it makes sense to become more familiar with them. Matrix Vocabular The matrix shown below has 2 rows and 3 columns. Its dimension is 2 × 3. Any element of the matrix can be located by specifying the row and column number in which is appears. � a 11 � a 12 a 13 a 21 a 22 a 23 Locating Elements Identify the element in each location. 1 The element in the 1st row, 2nd column 2 The element in the 2nd row, 3rd column

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Exploring a Matrix Since we’ve seen that matrices can be useful in solving equations, it makes sense to become more familiar with them. Matrix Vocabular The matrix shown below has 2 rows and 3 columns. Its dimension is 2 × 3. Any element of the matrix can be located by specifying the row and column number in which is appears. � a 11 � a 12 a 13 a 21 a 22 a 23 Locating Elements Identify the element in each location. 1 The element in the 1st row, 2nd column 2 The element in the 2nd row, 3rd column

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Exploring a Matrix Since we’ve seen that matrices can be useful in solving equations, it makes sense to become more familiar with them. Matrix Vocabular The matrix shown below has 2 rows and 3 columns. Its dimension is 2 × 3. Any element of the matrix can be located by specifying the row and column number in which is appears. � a 11 � a 12 a 13 a 21 a 22 a 23 Locating Elements Identify the element in each location. 1 The element in the 1st row, 2nd column 2 The element in the 2nd row, 3rd column

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Exploring a Matrix Since we’ve seen that matrices can be useful in solving equations, it makes sense to become more familiar with them. Matrix Vocabular The matrix shown below has 2 rows and 3 columns. Its dimension is 2 × 3. Any element of the matrix can be located by specifying the row and column number in which is appears. � a 11 � a 12 a 13 a 21 a 22 a 23 Locating Elements Identify the element in each location. 1 The element in the 1st row, 2nd column 2 The element in the 2nd row, 3rd column

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Exploring a Matrix Since we’ve seen that matrices can be useful in solving equations, it makes sense to become more familiar with them. Matrix Vocabular The matrix shown below has 2 rows and 3 columns. Its dimension is 2 × 3. Any element of the matrix can be located by specifying the row and column number in which is appears. � a 11 � a 12 a 13 a 21 a 22 a 23 Locating Elements Identify the element in each location. 1 The element in the 1st row, 2nd column ( a 12 ) 2 The element in the 2nd row, 3rd column

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Exploring a Matrix Since we’ve seen that matrices can be useful in solving equations, it makes sense to become more familiar with them. Matrix Vocabular The matrix shown below has 2 rows and 3 columns. Its dimension is 2 × 3. Any element of the matrix can be located by specifying the row and column number in which is appears. � a 11 � a 12 a 13 a 21 a 22 a 23 Locating Elements Identify the element in each location. 1 The element in the 1st row, 2nd column ( a 12 ) 2 The element in the 2nd row, 3rd column

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Exploring a Matrix Since we’ve seen that matrices can be useful in solving equations, it makes sense to become more familiar with them. Matrix Vocabular The matrix shown below has 2 rows and 3 columns. Its dimension is 2 × 3. Any element of the matrix can be located by specifying the row and column number in which is appears. � a 11 � a 12 a 13 a 21 a 22 a 23 Locating Elements Identify the element in each location. 1 The element in the 1st row, 2nd column ( a 12 ) 2 The element in the 2nd row, 3rd column ( a 23 )

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Another Example Example Use the matrix A below to answer the following questions.   1 7 5 A = 2 4 3   − 1 4 0 1 What is the dimension of this matrix? 2 What is the entry in the 1st row, 2nd column? 3 What is the entry in the 3rd row, 1st column?

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Another Example Example Use the matrix A below to answer the following questions.   1 7 5 A = 2 4 3   − 1 4 0 1 What is the dimension of this matrix? 2 What is the entry in the 1st row, 2nd column? 3 What is the entry in the 3rd row, 1st column?

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Another Example Example Use the matrix A below to answer the following questions.   1 7 5 A = 2 4 3   − 1 4 0 1 What is the dimension of this matrix? (3 × 3) 2 What is the entry in the 1st row, 2nd column? 3 What is the entry in the 3rd row, 1st column?

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Another Example Example Use the matrix A below to answer the following questions.   1 7 5 A = 2 4 3   − 1 4 0 1 What is the dimension of this matrix? (3 × 3) 2 What is the entry in the 1st row, 2nd column? 3 What is the entry in the 3rd row, 1st column?

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Another Example Example Use the matrix A below to answer the following questions.   1 7 5 A = 2 4 3   − 1 4 0 1 What is the dimension of this matrix? (3 × 3) 2 What is the entry in the 1st row, 2nd column? (7) 3 What is the entry in the 3rd row, 1st column?

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Another Example Example Use the matrix A below to answer the following questions.   1 7 5 A = 2 4 3   − 1 4 0 1 What is the dimension of this matrix? (3 × 3) 2 What is the entry in the 1st row, 2nd column? (7) 3 What is the entry in the 3rd row, 1st column?

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Another Example Example Use the matrix A below to answer the following questions.   1 7 5 A = 2 4 3   − 1 4 0 1 What is the dimension of this matrix? (3 × 3) 2 What is the entry in the 1st row, 2nd column? (7) 3 What is the entry in the 3rd row, 1st column? ( − 1)

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Special Types of Matrices Two types of matrix are of particular interest. Row Vector A row vector is a 1 × n matrix where n is any integer greater than zero. Column Vector A column vector is an n × 1 matrix where n is any integer greater than zero. An Example Column Vector An Example Row Vector The matrix below is a 2 × 1 The matrix below is a 1 × 4 column vector. row vector. � 2 � V = � � U = 1 2 4 − 3 3

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Special Types of Matrices Two types of matrix are of particular interest. Row Vector A row vector is a 1 × n matrix where n is any integer greater than zero. Column Vector A column vector is an n × 1 matrix where n is any integer greater than zero. An Example Column Vector An Example Row Vector The matrix below is a 2 × 1 The matrix below is a 1 × 4 column vector. row vector. � 2 � V = � � U = 1 2 4 − 3 3

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Special Types of Matrices Two types of matrix are of particular interest. Row Vector A row vector is a 1 × n matrix where n is any integer greater than zero. Column Vector A column vector is an n × 1 matrix where n is any integer greater than zero. An Example Column Vector An Example Row Vector The matrix below is a 2 × 1 The matrix below is a 1 × 4 column vector. row vector. � 2 � V = � � U = 1 2 4 − 3 3

The Basics of Matrices Matrix Addition Scalar Multiplication Conclusion Special Types of Matrices Two types of matrix are of particular interest. Row Vector A row vector is a 1 × n matrix where n is any integer greater than zero. Column Vector A column vector is an n × 1 matrix where n is any integer greater than zero. An Example Column Vector An Example Row Vector The matrix below is a 2 × 1 The matrix below is a 1 × 4 column vector. row vector. � 2 � V = � � U = 1 2 4 − 3 3