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Questions and Answers
What is a matrix?
A matrix is a rectangular array of numbers written within brackets.
What is the size of a matrix with m rows and n columns called?
m x n matrix
What is a square matrix?
A square matrix is a matrix with n rows and n columns.
A row matrix has only one column.
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Which of the following statements is true about a column matrix?
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What is the principal diagonal in a matrix?
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What defines a zero matrix?
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What is an identity matrix?
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Define a scalar matrix.
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The transpose of a matrix swaps its rows and columns.
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The transpose of a matrix A is denoted by ______.
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How do you determine if a matrix is a diagonal matrix?
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What is a 3 x 3 scalar matrix with all elements equal to 7?
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Find the transpose of a 2 x 2 identity matrix.
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Study Notes
Matrices
- A matrix is a rectangular arrangement of numbers enclosed in brackets.
- Each number in a matrix is an element.
- An m x n matrix has m rows and n columns.
Types of Matrices
- A square matrix has the same number of rows and columns.
- A column matrix has one column.
- A row matrix has one row.
- A vector is a matrix with one row or one column.
- A zero matrix has all elements equal to zero.
- A diagonal matrix is a square matrix with non-diagonal elements equal to zero.
- An identity matrix is a diagonal matrix with all diagonal elements equal to 1.
- A scalar matrix is a square matrix with a constant value on the diagonal and zeros elsewhere.
Position of Elements
- Elements are identified by their row and column, denoted using double subscript notation.
-
a_ijrepresents the element in row i and column j. - The principal diagonal consists of elements
a_iiwhere i is the row and column number.
Transpose
- The transpose of a matrix
Ais denotedA^T. - It is created by swapping the rows and columns of the original matrix.
- If the original matrix is
m x n, the transpose isn x m.
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Description
This quiz covers essential concepts related to matrices, including their definitions, types, and the position of elements within them. Understand the characteristics of square, column, row, zero, diagonal, identity, and scalar matrices, as well as the notation used to identify elements. Test your knowledge of matrix transposition and element positioning.
