OPERATIONS ON MATRICES

Front

What is a matrix?

Back

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

Front

What does it mean to add two matrices?

Back

To add two matrices, they must have the same dimensions, and you add corresponding elements.

Front

What is the result of adding the matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]?

Back

A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]]

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

If A = [[1, 2], [3, 4]], what is A^T?

Back

A^T = [[1, 3], [2, 4]]

Front

What is matrix multiplication?

Back

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

Front

Can you multiply two matrices of different dimensions?

Back

No, the number of columns in the first matrix must equal 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.

Front

What is the determinant of a 2x2 matrix [[a, b], [c, d]]?

Back

The determinant is calculated as ad - bc.

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^(-1), such that A * A^(-1) = I, where I is the identity matrix.