WEBVTT
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Given that 𝐴 and 𝐵 are these matrices, find 𝐴 plus 𝐵 times 𝐴.
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So to follow the order of operations, we need to add 𝐴 and 𝐵 first and then that we will multiply by 𝐴.
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So in order to add these, we will add numbers in the corresponding spots.
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So for example, negative five and four are both on the top left-hand corner.
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Six and negative three are both on the first column, the bottom row.
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We will add negative five and six and then six plus five and now we simplify.
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So we have the 𝐴 plus 𝐵 as negative one, one, negative nine, eleven.
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And now we need to take that matrix and multiply by 𝐴.
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So multiplying the matrix that we got from 𝐴 plus 𝐵, we’re now multiplying that by 𝐴.
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So multiplying matrices is different than adding.
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Before we begin multiplying, let’s decide how big our matrix should be.
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These are both two-by-two matrices and the two inside numbers should be exactly the same; if they’re not, it won’t work.
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So here we do have that.
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And then the outside twos will be the size of the product, so the actual size of our final answer matrix.
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So just like with adding, we multiply the first two numbers together in the top left-hand corner, but we also add one times negative six.
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This will be our very first number.
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So we’ll have to add those together; that will be our first number.
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And it will be on the top left-hand corner of our final matrix.
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Now below it, still in column number one, we take negative nine times negative five and then we add.
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Eleven times negative six, this will be our second number in column number one.
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So notice we’re taking the first two rows which are the only two rows in our product of 𝐴 plus 𝐵, that matrix, and we’re multiplying by the first column in 𝐴, this negative five, negative six.
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So now to get our other numbers in column number two for our final answer, we will multiply by this column instead.
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So we take negative one times negative five and one times six.
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And now it’s the same thing, but for the second row.
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So we take negative nine times negative five and eleven times six and now we simplify.
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So we went ahead and multiplied all the numbers together.
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And now to simplify, we’ll add each of these numbers together.
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Therefore, after multiplying by 𝐴, our final matrix would be negative one, 11 negative 21, 111.
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So again, we added 𝐴 and 𝐵 together and then we multiply it by 𝐴 and that gives us our final matrix.