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Questions and Answers
What is a matrix defined as?
What is a matrix defined as?
- A set of mn quantities arranged in a circular array
- A set of mn quantities arranged in a rectangular array (correct)
- A collection of numbers in random order
- A geometric representation of numbers
When can two matrices A and B be added together?
When can two matrices A and B be added together?
- If they have at least one element in common
- If they are of different orders
- If they are of the same order (correct)
- If they contain the same number of rows
Which of the following is true about the equalities of matrices?
Which of the following is true about the equalities of matrices?
- Two matrices are equal if they have the same order and all corresponding elements are equal (correct)
- Matrices can be equal even if they have different orders
- Equality of matrices depends on their shape rather than their elements
- Two matrices are equal only if all corresponding elements are different
What is the result of multiplying a matrix A by a number 3, if A is given as follows: A = ((1, 2, 3), (0, -1, 2))?
What is the result of multiplying a matrix A by a number 3, if A is given as follows: A = ((1, 2, 3), (0, -1, 2))?
What is a null matrix?
What is a null matrix?
Flashcards
Matrix Definition
Matrix Definition
A rectangular arrangement of numbers (elements) in rows and columns; denoted by a single letter, enclosed in brackets.
Matrix Addition
Matrix Addition
Adding matrices involves adding corresponding elements of matrices of the same order; the result is a matrix of the same order.
Matrix Subtraction
Matrix Subtraction
Subtracting matrices involves subtracting corresponding elements of matrices of the same order; the resultant is a matrix of the same order.
Equal Matrices
Equal Matrices
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Null Matrix
Null Matrix
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Study Notes
Matrices
- A matrix is a rectangular array of numbers
- Useful for representing and performing calculations on multiple values
- Matrices are useful for solving systems of linear equations
- Denotes an array of numbers with a single symbol for compact calculations
- Increasingly important in various scientific branches
Definition of a Matrix
- A matrix is an arrangement of elements in a rectangular array of rows and columns
- Enclosed by brackets (e.g., [])
- Designated by a letter (e.g., A)
- Elements are denoted by a₁ⱼ (e.g., A₁₁, A₁₂, etc.)
- Order of a matrix is (m x n), where m = number of rows, n = number of columns
- A square matrix has the same number of rows and columns (m = n)
Elements of a Matrix
- Individual quantities within a matrix
- Identified by their row number (i) and column number (j)
- Represented as aᵢⱼ
Matrix Addition and Subtraction
- Matrices must be of the same order to add or subtract
- Elements of corresponding positions are added (or subtracted)
- New matrix C is formed with elements cᵢⱼ = aᵢⱼ ± bᵢⱼ
Matrix Multiplication
- A matrix product (AB) is defined when the number of columns in Matrix A is equal to the number of rows in Matrix B
- Product AB results in a matrix C of order (m x n)
- Elements of matrix C are calculated as cᵢⱼ = Σaᵢₛbₛⱼ (s = 1…p), where p is the number of columns of A
- Matrix multiplication is not commutative (AB ≠ BA) in general
Special Types of Matrices:
- Null Matrix: A matrix of any order with all elements equal to zero
- Unit or Identity Matrix (I): A square matrix with 1s along the main diagonal and 0s elsewhere
- Multiplication of a matrix by an Identity matrix results in the original matrix
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