Matrices Review

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 of 'rows x columns'. For example, a matrix with 3 rows and 2 columns is said to have dimensions 3 x 2.

Front

Can two matrices be multiplied?

Back

Two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Front

What is a 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 of the matrix.

Front

How do you calculate the determinant of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the determinant is calculated as ad - bc.

Front

What is scalar multiplication of a matrix?

Back

Scalar multiplication involves multiplying each entry of a matrix by a constant (scalar) value.

Front

What does it mean if the determinant of a matrix is zero?

Back

If the determinant of a matrix is zero, it indicates that the matrix is singular and does not have an inverse.

Front

What is the result of multiplying a matrix by a zero matrix?

Back

Multiplying any matrix by a zero matrix results in a zero matrix of appropriate dimensions.

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, turning rows into columns and vice versa.