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LLC Rhbela 0 1 | UAEIU#uu [l purticu...

Question

LLC Rhbela 0 1 | UAEIU#uu [l purticu

LLC Rhbela 0 1 | UAEIU#uu [l purticu



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Write without absolute value symbols. $$|-6 i|$$

Obviously, we want to use our equation of the fallen. So we first meet you were at this in the form A plus. Yeah. So what I can do is multiply this by its contract and divide by the number we have two minus. Do I? And in distance the difference of squares until we get one squared money, a new one. So we get to this is over too. So this is actually a one minus I. So it's here at this size one minus. I know. Using our equation, we get once word plus once worked. So that's equal to the square root of two.

In this question we have to use row reduction to find the invoices of the given mattresses if they exist. And check it by multiplication. Now let us consider It takes 111 011100. And on the right side identity metrics of all three. 100 010 001. Now they will pro radio steam metrics. We will apply the operation three store store Our 3 -11 and Arvin starts to Urban -R2. On applying these operations we got the metrics 100 011 0 -1 -1. And on the right side 1 -10 Vettel one vehicle -1 Little one. Now again we will apply the operation Our three stores too. I want to yeah on applying this operation regard the metrics one beetles, beetle, 011 000. And on the right side 1 -10. Mhm 01 zero -111. Mhm. Since we observe that left hand side of the metrics is not an identity matrix. Therefore inverse of matrix. There does not exist exist. Hence a singular romantic. Yeah. Okay. Thank you.

Office. So let's use our equation on this. This is 1/2 were first. You have 1/4. Good. It's where rid of this. So what does that we get 1/4 plus 1/16 which got into our yeah, 5/60 but at the square root of 5/16 which is equal to describe it of 5/4.

In discussion. We have to find out the the universal forgiven metrics. The given matrixes of uh three by three order which is equals two in the first row. The entries are 11 and one in the second row. The entries are 01 and one in the third row. The entries are 00 and one. Now, first of all we will consider the given metrics as This one metrics here 1, 11 01, one and 001. And here as the identity matrix of third order. So 100 010 001. Now we will use the roll reduction method to convert this. This given metrics into identity metrics and these metrics into whatever it becomes by applying the same operation to both the emergencies. So first of all yeah we will apply the cooperation for the first True as urban stores Are 1 -12 and Artist does are 2 -23. We will apply these operations mm And in subsequent steps So our two stores Our 2 -13. Now what we will get when we will apply the faster operation to these mattresses and we will get here. As first we will apply for the operation for Robin. We will get one minus zero as one and one minus one is zero. Again one minus one will be zero. And uh 2nd and 3rd row will be just same as it is sorry. In second row we will apply our two minus a tree. So this will be 0 0 and 1 0 again one and 1 -1 is zero And 3rd row will be as it is 00 and one. Now for this identity. Matics applying the same operations for Robin in Robin we will apply Robin minus throw too. So this will be one minus zero here. 10 minus one will be minus one And 0 0 will be zero. And for our two we will play our 2 -3. We will get 0 0 1 0 has one and 0 -1 will be here minus one. And tomorrow as it is. So 001. Now here this is identity metrics at the place of metrics A and this one a matrix must be the universe of metrics A. So we can write the universe of metrics A as a universe he calls to. This will be 1 -10 zero, one minus one And 001. So this will be the universe of these metrics. Now we will check that whether this universe's character not by multiplying this to the matrix. A. And if we get the identity matrix uh by the product of these two mattresses, then this is correct. So we will find out the product of A and a universe which should be an identity medics. So this will be here we calculate we are calculating eight times in verse and we will get it as 111, 011, 001. And the universe of metrics is 1 -100 and 01 -1001. Now on multiplying these matters is we will get eight times a universe as here when multiplying fast road to the first column of this universe, we will get one times one, so one times one plus one times zero And one time 0 again. So this will be one time zero. This will become one plus zero plus zero. This will be one only here. And now multiplying the first robot to the second column of this universe. We will get one times -1 Plus one times 1 and one times zero plus one times zero. We will get here minus one plus one which is zero and plus zero again zero. So this is zero. A normal deploying the first row to the 3rd column of the universe. We will get one time zero and one times minus one which will be minus one and one times one will be plus one. Now again, this zero minus one plus one will be zero. So zero for the third element. Now by multiplying the second row of eight to the first column of universe, we will get zero times one, zero times one and one times zero plus one times zero. And again, one time 0. So These all are zero. So this will again be zero and now I'm multiplying 2nd road to the second column of This universe. So we will get zero times -1. This will be zero and 1 times one which will be plus one and one time zero will be zero. So here's zero plus one plus zero will be one. Now multiplying second road to the third column of this universe and we will get zero times mm Here it will be zero times zero which is zero and one times minus one will be minus one and one times one will be plus one which results in zero. So this is zero. Now we will multiply row three to the first column of this universe. You will get zero times one. So zero times one will be zero plus zero times zero will be zero Plus one times 0 will be against zero. So we get so this will be zero. And multiplying row 3 to the second column, We will get zero times -1. zero times -1 plus zero times one. Again one sorry zero Plus one times 1 sorry one time zero. So one time zero will be zero. These all are zero. So here this will be zero. And now multiplying rotary to the column. Third of university will get zero times zero and zero plus zero times minus one. This was zero times zero plus zero times minus one. This will be zero and 1 times one will be one. So this will result into one. So here it is one. So we got the product of a. and E in versus the identity medics of three x 3. And so we can verify that this universe of matter is correct. I hope all of you got discussion. Thank you.


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