### Video Transcript

The table below represents the
prices of some drinks in a cafe. The cafe owner changes the prices
of the drinks so that each drink is now two times its original price. Determine the matrix that
represents the new prices of the drinks.

A matrix is simply an array of
numbers. And so, if we define 𝐴 to be the
matrix that represents the old prices of the drinks, we can simply transfer each of
the numbers from our table in as shown. The order of this matrix is three
by two, since it has three rows and two columns. And so matrix 𝐴 is 1.5, 5.5, two,
8.5, 3.5, nine. We’re told that the prices of the
drinks changes so that the price of each drink is now two times its original
price. And so, we want to double. We want to multiply each element in
the matrix by two. We can represent this as two 𝐴,
since we know that when we multiply a matrix by a scalar, we multiply each of the
individual elements. So the matrix two 𝐴 represents the
new prices of the drinks. And its elements are two times 1.5,
two times 5.5, two times two, two times 8.5, two times 3.5, and two times nine.

Let’s complete this element by
element. Two times 1.5 is three. So three is the element in the
first row and first column. Then two times 5.5 is 11, two times
two is four, and two times 8.5 is 17. Two times 3.5 is seven, and two
times nine is 18, meaning the element in our third row and second column is 18. And so we’ve completed the matrix
that represents the new prices of the drinks. It’s three, 11, four, 17, seven,
18.