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Math Makes Sense 6
That's how we learned matrix multiplication. That's the same thing here. These x and y here are just scalar numbers. So 3 times x plus 2 times y is equal to 7. And then matrix multiplication here, minus 6 times x plus math makes sense 6 times y is equal to 6.
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That's just traditional matrix multiplication that we learned several videos ago. Minus 6x plus 6y is equal to 6. These x's and y's are just numbers.
They're just scalar numbers. They're not vectors or anything. We would just multiply them times both of these numbers. So hopefully you see that math makes sense 6 problem is the exact same thing as this problem. And you've maybe had an a-ha moment math makes sense 6, if you watched the previous video.
Because this matrix also represented the problem, where do we find the intersection of two lines? Where the two lines-- I'm just going to do it on the side here-- the intersection of the two lines, 3x plus 2y is equal to 7.
And minus 6x plus 6y is equal to 6. And so, I had drawn two lines.
And we said, what's the point of intersection, et cetera, et cetera. And it was represented by this problem.
But here, we have-- well I won't say a completely different problem, because we're learning they're actually very similar-- but here I'm doing a problem of, I'm trying to find what combination of the matrices a and b add up to the matrix c. But it got reduced to the same matrix representation. And so we can solve this math makes sense 6 same exactly way we solved this problem.
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If we call this the matrix a, let's figure out a inverse. So we get a inverse is equal to what?
It equals 1 over the determinant of a. The determinant of a is 3 times 6.
And we did this in the previous video. You swap these two numbers.