Matrices

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form of rows x columns (e.g., a 3x2 matrix has 3 rows and 2 columns).

Front

How do you multiply two matrices?

Back

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The resulting matrix will have dimensions equal to the number of rows of the first matrix and the number of columns of the second matrix.

Front

What is the dimension of a 7 x 3 matrix?

Back

A 7 x 3 matrix has 7 rows and 3 columns.

Front

How many columns are in a 5 x 4 matrix?

Back

A 5 x 4 matrix has 4 columns.

Front

What is a scalar in matrix multiplication?

Back

A scalar is a single number that can multiply a matrix, affecting each element of the matrix by that number.

Front

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

Back

The result of multiplying any matrix by a zero matrix is 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. It acts as the multiplicative identity in matrix multiplication.

Front

What is a 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 the determinant of a matrix?

Back

The determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties about the matrix, such as whether it is invertible.

Front

What does it mean for a matrix to be invertible?

Back

A matrix is invertible if there exists another matrix such that their product is the identity matrix.