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The table below represents the prices of some drinks in a cafe.
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The cafe owner changes the prices of the drinks so that each drink is now two times its original price.
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Determine the matrix that represents the new prices of the drinks.
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A matrix is simply an array of numbers.
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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.
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The order of this matrix is three by two, since it has three rows and two columns.
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And so matrix 𝐴 is 1.5, 5.5, two, 8.5, 3.5, nine.
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We’re told that the prices of the drinks changes so that the price of each drink is now two times its original price.
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And so, we want to double.
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We want to multiply each element in the matrix by two.
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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.
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So the matrix two 𝐴 represents the new prices of the drinks.
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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.
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Let’s complete this element by element.
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Two times 1.5 is three.
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So three is the element in the first row and first column.
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Then two times 5.5 is 11, two times two is four, and two times 8.5 is 17.
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Two times 3.5 is seven, and two times nine is 18, meaning the element in our third row and second column is 18.
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And so we’ve completed the matrix that represents the new prices of the drinks.
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It’s three, 11, four, 17, seven, 18.