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 an inverse matrix?

Back

An inverse matrix A^-1 of a matrix A is a matrix such that when multiplied with A, results in the identity matrix.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Front

How do you determine if two matrices are inverses?

Back

Two matrices A and B are inverses if AB = I and BA = I, where I is the identity matrix.

Front

What is matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix.

Front

What are the conditions 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 result of multiplying a 2x3 matrix by a 3x2 matrix?

Back

The result is a 2x2 matrix.

Front

How do you find the element a_23 in a matrix?

Back

The element a_23 is found in the 2nd row and 3rd column of the matrix.

Front

What is the determinant of a 2x2 matrix?

Back

For a matrix [[a, b], [c, d]], the determinant is ad - bc.