AA C&C Unit 5 FLASHCARD: Matrix Operations

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Front

Define the order of a matrix.

Back

The order of a matrix is defined by the number of rows and columns it contains, expressed as 'rows x columns'.

Front

What is the coefficient matrix of a system of equations?

Back

The coefficient matrix is a matrix that contains the coefficients of the variables in a system of linear equations.

Front

How do you find the inverse of a matrix?

Back

To find the inverse of a matrix A, you must find a matrix B such that AB = I, where I is the identity matrix.

Front

What does it mean for a matrix to be undefined?

Back

A matrix element is undefined if it does not exist in the context of the given matrix dimensions.

Front

What is matrix addition?

Back

Matrix addition involves adding corresponding elements of two matrices of the same order.

Front

What is matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix, and is only defined when the number of columns in the first matrix equals the number of rows in the second.

Front

What is a scalar multiplication of a matrix?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a single number).

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere, denoted as I.

Front

What is the determinant of a matrix?

Back

The determinant is a scalar value that can be computed from the elements of a square matrix, providing important properties about the matrix.