Question

Suppose A is a matrix and k is a positive integer. What does the notation Ak mean?

Answer 1

Scalar product

Explanation:

The scalar product of a matrix refers to the product of a matrix and a number. The scalar is used to multiply each element in the matrix to get the final vector. In the question the scalar is k which is a constant and the matrix is A.

in the example below 2 is the scalar

`2*\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]`

the final matrix will be

`\left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right]`