Mhm. Here we have given a metrics a physical too one 2 3, 4 over our. And metrics even is equal to 10 minus 11 Matrix E two is equal to 0110 and metrics E three is equal to minus 2001 Now we need to compute the product of mattresses, even E. two And a. three. Then we need to verify that there are elementary column operations, which transforms A. To even A. two, a. 2 And there's A two, A. 3. So we first multiply in the mathematics A with these even elementary mattresses. So it is given us follow. So solution is solution. Okay, lettuce. Let us find the product, find the product even. So let us find product even. So metrics a into metrics even symmetric is 1, 2, 3, 4 and Magics. Everyone is given as 10 -11. Now we multiply it and we get. So the first entry in 1st row is 1 -2 is -1, then second injury is two. Third entries 3 -4 is again -1 and four countries 4. So so therefore A. Even is equal to. So we get the product of matrix A and even is a one is equal to minus one, 2 -1 and four. Now we find the elementary column operation Which transformed a two a. 1. So you find the elementary calling operations which transform A two A. 1. So we need to take a matrix A which is is equal to 1234. So the elementary column operation which is applied is C1 is replaced by C one plus minus one times of C two. So it will be So 1 -2 is -1 than it is to Then 3 -4 is -1 and it is for which is nothing. But our metrics even hence it is verified. Hence it is very hard. It is verified that the product A one is same as the limited column operation, which we have used to transform A to even now moving to the next, we have To find the product A. two. So here, you know we no fine product E E two. So The product A two is given us. Mhm. So matrix A, symmetric A. Into metrics. You too, The mattress is 1, 2, 3, 4. And metrics you too is The first entry in row is zero one and the second entry in the second row is 10 The product is so one in 200 plus two into one is too, so it is too, Then here it is, one then here it is for and the last entry in this through in this product is uh three into one is three plus 400 00 So it will be three. Therefore, E two is equal to 214, 3. Now, we find the elementary column operation was transformed A two A. Two, you're fine. Elementary call them operation be transformed mm to e toe. So take matrix A. Is equal do 1234. So the elementary column operation used is C1 is replaced by C two. Does we get? The first column is 2 4, and the second column is voluntary. So this is nothing but our required obtained the product aid. Hence it is verified and it is very hard Now moving to the next, we need to compute the product A. three. So the metrics, he's now we compute we compute for firing the product mm A three, sorry, So N two E 3, metrics is 12341234 And metrics E three, he's given it minus 20 01 So the output is So it will be -2. The first Entries -2. The second entries too, The 3rd entry is -6, fourth entries for therefore a three is equal to minus two minus 64 Yeah, no, the elementary elementary column operation we transform which transformed mm to E three is given us is given us. So we need to find The elementary collaboration. So metrics is 1, 2, 3, 4. No, we apply a column transformation given us C1 is replaced by -2 times up, see one. So it will be minus two, two minus six and full, which is nothing but which is nothing But our obtained product A three. Hence it is verified The adopting correct a. three. And the column operation used his to find the output is same. Has it is verified? Thus, it is our required solution.