Questions and Answers
Define what a matrix is.
A matrix is a rectangular array of elements.
Identify special types of matrices.
Row Vector, Diagonal Matrix, Column Vector, Identity Matrix, Submatrix, Zero Matrix, Square Matrix, Tri-diagonal, Upper Triangular Matrix, Lower Triangular Dominant Matrix.
Identify when two matrices are equal.
Two matrices are equal when they have the same dimensions and corresponding elements are equal.
What is a vector?
Signup and view all the answers
Which of the following is an example of a row vector?
Signup and view all the answers
Identify an upper triangular matrix:
Signup and view all the answers
Give an example of a square matrix.
Signup and view all the answers
What is the size of matrix [A] with 3 rows and 4 columns?
Signup and view all the answers
Study Notes
Definition of a Matrix
- A matrix is a rectangular array of elements, which can include symbolic expressions or numbers.
- Denoted mathematically as
[ A]
, each entry is referred to as an element and is represented asaij
, wherei
is the row number andj
is the column number.
Types of Matrices
-
Row Vector: A matrix with one row, denoted as
[ B] = [b1 b2 ... bn]
. -
Column Vector: A matrix with one column, denoted as
[C] = [ c1 ] [ c2 ] [ ... ] [ cm ]
-
Square Matrix: A matrix where the number of rows
m
is equal to the number of columnsn
. Diagonal elements are referred to asa11, a22, ..., ann
. - Zero Matrix: A matrix where all elements are zero.
- Diagonal Matrix: A square matrix where all off-diagonal elements are zero.
- Identity Matrix: A diagonal matrix where all diagonal elements are 1.
- Upper Triangular Matrix: A matrix where all elements below the main diagonal are zero.
- Lower Triangular Matrix: A matrix where all elements above the main diagonal are zero.
- Tri-diagonal Matrix: A matrix that only has non-zero elements on the main diagonal and the diagonals directly above and below it.
- Dominant Matrix: A matrix where each diagonal element is greater than the sum of the absolute values of the other elements in its row.
Matrix Size
- The size of a matrix
[A]
is denoted bym×n
, indicatingm
rows andn
columns. For a matrix with 3 rows and 4 columns, the size is3×4
.
Matrix Equality
- Two matrices are equal if they have the same dimensions and corresponding elements are equal.
Submatrices
- A submatrix is formed by deleting some rows and/or columns from a matrix, without removing any rows or columns completely.
Example Matrices
- Illustration of tire sales data represented in matrix form showing sales by tire brands over four quarters.
- Example matrices include a row vector
[ B] = [25 20 3 2 0]
and a column vector[C] = [25] [5] [6]
Additional Key Points
- Identifying sales in a matrix, such as finding the number of Copper tires sold in Quarter 4 by referencing the corresponding row and column.
- Key features of specific matrix types like identifying upper triangular matrices through the positioning of zeros below the diagonal.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers the fundamentals of matrices, including their definitions and special types. You will also learn how to determine when two matrices are equal. Understanding matrices is essential for various applications in mathematics and data presentation.