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Flashcards on Matrices
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What is a matrix?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
How are matrices represented?
Matrices are typically represented by capital letters.
What is the order of a matrix?
The order of a matrix is the number of rows and columns it has, represented as 'rows × columns'.
What is a square matrix?
A square matrix has an equal number of rows and columns.
What is the identity matrix?
The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere.
Define matrix addition.
Matrix addition involves adding corresponding elements of two matrices of the same order.
What is matrix subtraction?
Matrix subtraction involves subtracting corresponding elements of two matrices of the same order.
Define scalar multiplication of a matrix.
Scalar multiplication of a matrix involves multiplying each element of the matrix by a scalar (a single number).
What is the transpose of a matrix?
The transpose of a matrix is obtained by interchanging its rows with columns.
What is matrix multiplication?
Matrix multiplication involves multiplying rows of the first matrix with corresponding columns of the second matrix.
What is the determinant of a matrix?
The determinant of a matrix is a scalar value that is computed from the elements of the matrix.
What is an inverse matrix?
An inverse matrix is a matrix that, when multiplied with the original matrix, yields the identity matrix.
What are symmetric matrices?
Symmetric matrices are square matrices that are equal to their own transpose.
What are skew-symmetric matrices?
Skew-symmetric matrices are square matrices that are equal to the negation of their own transpose.
What are upper triangular matrices?
Upper triangular matrices have all elements below the main diagonal equal to zero.
What is a matrix?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
How are matrices represented?
Matrices are typically represented by capital letters.
What is the order of a matrix?
The order of a matrix is the number of rows and columns it has, represented as 'rows × columns'.
What is a square matrix?
A square matrix has an equal number of rows and columns.
What is the identity matrix?
The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere.
Define matrix addition.
Matrix addition involves adding corresponding elements of two matrices of the same order.
What is matrix subtraction?
Matrix subtraction involves subtracting corresponding elements of two matrices of the same order.
Define scalar multiplication of a matrix.
Scalar multiplication of a matrix involves multiplying each element of the matrix by a scalar (a single number).
What is the transpose of a matrix?
The transpose of a matrix is obtained by interchanging its rows with columns.
What is matrix multiplication?
Matrix multiplication involves multiplying rows of the first matrix with corresponding columns of the second matrix.
What is the determinant of a matrix?
The determinant of a matrix is a scalar value that is computed from the elements of the matrix.
What is an inverse matrix?
An inverse matrix is a matrix that, when multiplied with the original matrix, yields the identity matrix.
What are symmetric matrices?
Symmetric matrices are square matrices that are equal to their own transpose.
What are skew-symmetric matrices?
Skew-symmetric matrices are square matrices that are equal to the negation of their own transpose.
What are upper triangular matrices?
Upper triangular matrices have all elements below the main diagonal equal to zero.
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