matrices

Front

What is a matrix?

Back

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

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form 'm x n', where 'm' is the number of rows and 'n' is the number of columns.

Front

What is a scalar matrix?

Back

A scalar matrix is a square matrix in which all the elements are equal to the same scalar value.

Front

What is matrix addition?

Back

Matrix addition is the operation of adding two matrices by adding their corresponding elements. This is only possible if the matrices have the same dimensions.

Front

What is matrix multiplication?

Back

Matrix multiplication involves multiplying two matrices by taking the dot product of rows and columns. The number of columns in the first matrix must equal the number of rows in the second.

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 serves as the additive identity in matrix addition.

Front

What is 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 a determinant?

Back

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

Front

What is an inverse matrix?

Back

An inverse matrix is a matrix that, when multiplied with the original matrix, yields the identity matrix. Not all matrices have inverses.