Matrices Practice

Front

What is the dimension of a matrix?

Back

The dimension of a matrix is defined by the number of rows and columns it contains, expressed as 'rows x columns'. For example, a matrix with 3 rows and 2 columns is said to have a dimension of 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 matrix addition?

Back

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

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

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, meaning it does not have an inverse.

Front

How do you find the product of two matrices?

Back

To find the product of two matrices, multiply the rows of the first matrix by the columns of the second matrix, summing the products.

Front

What is a singular matrix?

Back

A singular matrix is a square matrix that does not have an inverse, which occurs when its determinant is zero.

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 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.

Front

What is a scalar multiplication of a matrix?

Back

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