Matrix Operations

Front

What is a matrix?

Back

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

Front

How do you determine the dimensions of a matrix?

Back

The dimensions of a matrix are given by the number of rows and columns it has, expressed as 'rows x columns'.

Front

What is the result of adding two matrices?

Back

The result of adding two matrices is another matrix where each element is the sum of the corresponding elements of the original matrices.

Front

What must be true in order to ADD two matrices?

Back

The dimensions of the two matrices must be equal.

Front

What is a scalar in matrix operations?

Back

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

Front

How do you multiply a matrix by a scalar?

Back

To multiply a matrix by a scalar, multiply each element of the matrix by that scalar.

Front

What is the result of multiplying two matrices?

Back

The result of multiplying two matrices is a new matrix where each element is calculated as the dot product of the corresponding row and column.

Front

What is the condition for matrix multiplication to be defined?

Back

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, acting as the multiplicative identity in matrix multiplication.

Front

What is the transpose of a matrix?

Back

The transpose of a matrix is formed by swapping its rows and columns.