Matrix Operations

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

What is the determinant of a matrix?

Back

The determinant is a scalar value that is a function of the entries of a square matrix, providing important properties such as whether the matrix is invertible.

Front

What does it mean for a matrix to be invertible?

Back

A matrix is invertible if there exists another matrix such that their product is the identity matrix.

Front

How do you add two matrices?

Back

You can add two matrices if they have the same dimensions by adding their corresponding elements.

Front

What is a scalar in relation to matrices?

Back

A scalar is a single numerical value that can multiply a matrix, affecting all its elements.

Front

What is the product of a matrix and a scalar?

Back

The product of a matrix and a scalar is obtained by multiplying each element of the matrix by the scalar.

Front

What is the condition for matrix multiplication to be defined?

Back

Matrix multiplication is defined when the number of columns in the first matrix equals the number of rows in the second matrix.

Front

What is the identity matrix?

Back

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

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is obtained by flipping it over its diagonal, switching the row and column indices.

Front

What is the zero matrix?

Back

The zero matrix is a matrix in which all elements are zero, serving as the additive identity in matrix addition.