WEBVTT
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Given that 𝐴 equals the matrix negative six, one, negative five, five, find 𝐴 squared.
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Okay, so to find 𝐴 squared, what we’re gonna be doing, is we’re gonna be multiplying the matrix negative six, one, negative five, five by itself.
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And I’ve set it out here so that we can actually see that I’m multiplying one matrix by another matrix.
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I’ve also circled here the dot between them.
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And that’s just to tell you that this dot, that actually means multiply, is telling us that we’re actually multiplying these two matrices together.
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Now the first thing to know, is that when we multiply a two-by-two matrix by a two-by-two matrix, the answer is also gonna be a two-by-two matrix.
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Okay, now when we’re actually looking what we’re going to multiply, we’re gonna be multiplying rows by columns.
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So actually, what we’re gonna be doing is when we multiply this row by this column, is we’re actually gonna be multiplying the corresponding members.
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So for example, we’re gonna start with negative six multiplied by negative six cause that’s the first term in our row multiplied by the first term in our column.
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And then we’re going to add to it.
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And you always add.
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It’s gonna be one multiplied by negative five cause that’s the second term in our first row and our second term in our first column.
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Okay, great.
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So we can now find out the value.
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So this is all equal to 31.
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And so that means, we’ve now found the first term in our matrix.
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Now we can move on to the second term.
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And this time what we’re gonna do is, we’re gonna multiply our first row by our second column.
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So we’ve got negative six, one multiplied by one, five.
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Again, we’re multiplying corresponding members.
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So for instance, we multiply the negative six by the one cause it’s the first term in our first row.
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And then this one is the first term in our second column.
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And then we’ve got one times five.
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And again, we add them.
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And we get the answer negative one.
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So this is gonna be the next term in our matrix.
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Okay, so now for the bottom-left term, what we’re gonna do, is we’re gonna multiply our second row by our first column.
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So we’re gonna get negative five, five multiplied by negative six, negative five.
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Again, just cause I’m reminding, the-the dot we’re using here is the same.
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It means multiply.
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So it’s also called the dot product.
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So we’re gonna get negative five multiplied by negative six plus five multiplied by negative five, which gives us an answer of five.
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So great, one more term added to our matrix.
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Right for the final value, we’re gonna multiply the second row by the second column.
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So it’s gonna be negative five, five multiplied by one, five which is gonna give us negative five multiplied by one plus five multiplied by five, which is all equal to 20.
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So therefore, we can say our final value is gonna be 20.
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And therefore, we can say our final answer is that 𝐴 squared is equal to the matrix 31, negative one, five, 20.