9-3c Flashcard (30)

Front

What is matrix multiplication?

Back

Matrix multiplication is an operation that takes two matrices and produces a third matrix. The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

What does A - B represent in matrix operations?

Back

A - B represents the element-wise subtraction of matrix B from matrix A, where both matrices must have the same dimensions.

Front

How do you add two matrices?

Back

To add two matrices, you add their corresponding elements. The matrices must have the same dimensions.

Front

What is the condition for multiplying a [2x3] matrix?

Back

A [2x3] matrix can only be multiplied by a [3xN] matrix, where N can be any positive integer.

Front

What is the product of two matrices?

Back

The product of two matrices is a new matrix obtained by multiplying rows of the first matrix by columns of the second matrix.

Front

Define a scalar in the context of matrices.

Back

A scalar is a single number that can multiply a matrix, affecting each element of the matrix.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all elements are zero. It acts as the additive identity in matrix addition.

Front

Explain the transpose of a matrix.

Back

The transpose of a matrix is obtained by flipping it over its diagonal, turning rows into columns and vice versa.

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.