Matrix Operations

Front

What are matrix operations?

Back

Matrix operations are mathematical procedures that involve matrices, including addition, subtraction, multiplication, and finding the determinant or inverse.

Front

How do you add two matrices?

Back

To add two matrices, they must have the same dimensions. You add corresponding elements from each matrix.

Front

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

Back

Multiplying a matrix by a scalar involves multiplying each element of the matrix by that scalar.

Front

What is the definition of a square matrix?

Back

A square matrix is a matrix that has the same number of rows and columns.

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 the determinant of a 2x2 matrix?

Back

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

Front

How do you find the inverse of a 2x2 matrix?

Back

The inverse of a 2x2 matrix [[a, b], [c, d]] is given by (1/det) * [[d, -b], [-c, a]], where det = ad - bc and det ≠ 0.

Front

What is matrix multiplication?

Back

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

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all elements are zero.

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.