Questions and Answers
Match the sentences with the correct words.
A(n) __________ is a rectangular array of numbers. = matrix A number in a matrix is called a(n) __________. = element Another name for an element of a matrix is a(n) __________. = entry
Match the sentences with the correct words.
A(n) __________ is all of the numbers in one horizontal line in a matrix. = row A(n) __________ is all of the numbers in one vertical line in a matrix. = column The __________ is the number of rows and the number of columns in a matrix. = dimension A related matrix formed by making the rows of a matrix into columns and the columns into rows is called a(n) __________. = transpose
What is the value of X₂,₄ in the matrix X?
9
What is the value of X₃,₂ in the matrix X?
Signup and view all the answers
What is the value of X₃,₄ in the matrix X?
Signup and view all the answers
What is the dimension of the transpose matrix Y?
Signup and view all the answers
What is the dimension of the transpose matrix C?
Signup and view all the answers
What is the dimension of the transpose matrix F?
Signup and view all the answers
What is g(x) if f(x) = -3x - 6?
Signup and view all the answers
What is g(x) if f(x) = 7x - 3?
Signup and view all the answers
What is g(x) if f(x) = -4x - 1?
Signup and view all the answers
The __________, designated 0ₘ×ₙ, is the m × n matrix, all of whose entries are 0.
Signup and view all the answers
Only matrices of the same __________ can be added or subtracted.
Signup and view all the answers
The __________ of a matrix is the matrix composed of the opposites of each entry in a matrix.
Signup and view all the answers
What is the result of adding [5 2 1 -4] and [-2 -2 -5 2]?
Signup and view all the answers
What is the result of adding [1 -2 2] and [-2 2 1]?
Signup and view all the answers
What is the result of subtracting [0 2 -1 -2] and [-6 5 -3 7]?
Signup and view all the answers
What is the result of subtracting [7 6 5 4] and [-2 -3 -4 -5]?
Signup and view all the answers
What is the correct matrix to complete this equation? [9 3 -3 -2] + [__ __ __ __] = [0 0 0 0]
Signup and view all the answers
What is the correct matrix to complete this equation? [4 0 8 -2] + [__ __ __ __] = [0 0 0 0]
Signup and view all the answers
What is the correct matrix to complete this equation? [7x + 3 = 5] and [y - 1 = 6]
Signup and view all the answers
What is the correct matrix to complete this equation? [4x + 5 = -4] and [y - 3 = 2]
Signup and view all the answers
What is the algebraic definition that describes the piecewise graph for (-3, -1), (-1, 1), (1, 3)?
Signup and view all the answers
Study Notes
Matrix Fundamentals
- A matrix is defined as a rectangular array of numbers, with elements being individual numbers within the matrix.
- Each entry in a matrix can be referred to as an element.
Matrix Structure
- A row consists of numbers arranged horizontally within a matrix, while a column consists of numbers arranged vertically.
- The dimension of a matrix is indicated by the number of rows and columns it has.
- The transpose of a matrix switches its rows and columns, resulting in a new matrix.
Specific Matrix Examples
- In matrix X, located at position (2,4), the entry is 9, while entry (3,2) displays 4, and entry (3,4) is 12.
- The dimensions of the transpose matrix Y are specified as 4×3.
Matrix Operations
- The zero matrix, designated 0ₘ×ₙ, has all entries equal to 0 and is applicable to matrices of identical dimensions for addition or subtraction.
- Matrix addition combines corresponding elements from two matrices of the same dimensions.
- Subtraction of matrices involves subtracting corresponding elements, yielding new matrices.
Solving for Missing Entries
- Equations can be solved for missing matrices by ensuring the resulting sum equals a zero matrix.
Standard Form Equations
- The combination of linear equations can be expressed in standard form. For instance, the equations 7x + 3 = 5 and y - 1 = 6 can be combined into the equation 7x - y = -5.
- Similarly, equations 4x + 5 = -4 and y - 3 = 2 can be combined to yield the equation 4x - y = -14.
Piecewise Function Definition
- A piecewise function can be described using defined intervals. For example, the points (-3, -1), (-1, 1), and (1, 3) correspond to the function definition based on specific domains.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Explore the basics of matrices including their definitions, structures, and operations. This quiz covers matrix dimensions, transpose concepts, and various operations like addition and subtraction. Test your understanding of these essential algebraic structures!
