5

Find PT # 0 8) 10i0...

Question

Find PT # 0 8) 10i0

find PT # 0 8) 1 0i0



Answers

Divide. $$0 . 8 \longdiv { 1 0 . 8 4 }$$

Okay. We want to compute the product off. These teammates sees this actually identity here. So we're gonna be end up left with just this. But I will do the whole more progression out for you so you can see what's happening. So what did you make? A modification? You do the rows of the first matrix against the columns of the 2nd 1 for each respective element. So, for example, first row First column, first row against the first car. So here you've got four times, 10 times by eight. So we left for you. Stick with the first road. So it's that's where the first Matrix, but then moving on the second column. So get taken. Second coming out second matrix. But I fall off the zero and want a blocked off that ate said for 31st right. Second column. We just for the night now moving on to our second row. First column. One. Not that 90 lots. That minus two on second row. Second column. What zero is that? Nine. And just one long at minus two. As we hypothesized earlier, these are the same on this is our product

Okay, so we have zero plus and we're adding zero to number. So that's this equal to that number. That's negative eight.

Okay, so to do matrix multiplication on these two matrices, we start in the first row of our first matrix. So starting right here and the first column of our second matrix. So right here, we need to find the dot product of these two of this row in this column. And basically, that just means we take the first term of each the product of the first term of each plus the product of the second term. And that's our dot product. So that means we'll be doing one. Times two is two, but negative. One times three is negative. Three to plus negative three gives us negative one. So that was in our first position of our resulting matrix. Now we leave our row pointer in the same row in the first Matrix. We're gonna shift our column pointer to the second column now. Same process. Now we have one times eight plus negative One time, six So minus six eight minus six is, too. That goes in the next position in our matrix shift. Our column pointer again. Now we have one times negative. One is negative. One and negative. One time zero, which is zero negative one plus zero is negative one to replacing negative one in toe resulting matrix. Now we've gone through all of the columns of our second matrix. So we're going to move on to our next row in the first Matrix. We're going back to the first column in the second Matrix. And this also signals that we're moving to a new row in our resulting matrix. And now we're filling up the second row instead of the first. So we have negative three times to his negative. Six, two times three is positive. Six Negative six plus 60 Moving on to the second column. Negative. Three. Tens eight is negative. 24 Two times six is positive. 12 Negative. 24 plus 12 gives us a negative 12. Now, we're in the third time of the second Matrix. Uh, negative. Three times negative ones. Positive. Three, two times zero is 03 plus zero is three. Now we've gone through all of our columns again. So we're moving on to our final row in the first Matrix back to the first column in the second Matrix, and we have zero times 20 plus five times 3 15 plugging in 15. You'll notice that we're always going to have a zero for the first term in this row. And that's always gonna be multiplied on the same position in each of the columns and the second vector. So the zero times it'll be 00 times negative one will be zero eso weaken. Just skip that stuff, will. No, it'll always be zero plus the dot product of the second component of each are the product of the second component of each tool. We'll just do five times six is 30 0 plus 30 30. Now, in the third column again, we're gonna have zero times negative one and zero. And then we also have five times zero is another zero. So zero plus zero is just zero. No, he's gone through all three columns for all three of our rose, which means that we have finished and this is our resulting matrix

In this example, we're going to be performing the matrix multiplication that we see displayed here. The first Matrix is of size three by two, since it has three rows, two columns and the Second Matrix has two rows three columns, so it's of size to buy three. We have a match in the inner dimensions, so this product is well defined and the size of the product will be three by three, taken from these outer dimensions. So let me form a three by three matrix, and our first goal here is now to calculate. Column one. We fix our attention to column one of the second Matrix and go row by row, starting with one negative one so will multiply one times two plus negative one times three. So this gives us all together too minus three for a negative one, which copies here. Now, when we go to the next steps of this pattern, it's important to notice that this to this three and this or excuse me, the two in the three here, which came from the first column, won't be changing. So it's just copy to three and then again to three with space between them. Now we go to our second row here from the first Matrix, which is negative. Three, which will multiply here, plus two times the entry. Three. There we obtain negative six plus six for a entry zero. And now we go to the second. Or excuse me, the third row, which has entry 05 So places zero here plus puts five here and multiply. And we obtained 15. So that's our third entry for that column. Now we have a copy. The same kind of pandering to build this second column. We go to the second column of the Second Matrix, which has 86 Let me write 86 twice. And now, or rather three times altogether. And now we go and focus our attention to the first row. One negative one place one here and negative one here. Then we have eight minus six, resulting in a two two copies in there. Now focus on negative three to the second row. We place a negative three here, plus two goes here. So this is now negative. 24 plus 12 resulting in negative 12. So that's our next entry. Then from 05 we'll place a zero here and five here multiplying those entries in green. So this gives us 30 altogether, and that means 30 will copy Here. Now, we're onto the very last column to build this column. We now focus on this column here with negative 10 And as before, let me write this in three for three times. So negative 10 with some space. Then we focus our attention once again on the first row, second row and third row. So start with one negative one. Well, multiply by one here and take negative one time. Zero. This gives us a negative one entry. Now we're on to row two with a negative three to sell. Put here. Negative. Three multiplying. Negative. One plus two multiplying zero. This gives us a positive three. And now we're on to the final row. 05 Take zero times negative. One plus five times zero, and we produce a zero, which copies? In here. So this is the computation of these two matrix sees multiplied together


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