Video: Determining the Matrix That Represents a Given Set of Data

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.

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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.

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