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 is the order of a matrix?

Back

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

Front

What is matrix addition?

Back

Matrix addition involves adding corresponding elements of two matrices of the same order to produce a new matrix.

Front

What is matrix subtraction?

Back

Matrix subtraction involves subtracting corresponding elements of two matrices of the same order to produce a new matrix.

Front

What is scalar multiplication of a matrix?

Back

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

Front

What is matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix, and the resulting matrix's element is the sum of these products.

Front

What are the conditions for matrix multiplication?

Back

For two matrices A (of order m x n) and B (of order n x p) to be multiplied, the number of columns in A must equal the number of rows in B.

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, such that AI = A for any matrix A.

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A⁻¹, such that AA⁻¹ = I, where I is the identity matrix.

Front

How do you determine if a matrix has an inverse?

Back

A matrix has an inverse if it is square and its determinant is non-zero.