00:01
Hi, in this question we need to check whether the given system is consistent or not.
00:08
For that first to fall we will write the augmented matrix that would be equals to as matrix 4 minus 1 3, 209 146 and on the right side we have 12 minus 5 minus 5 minus 6.
00:40
Minus 32.
00:43
Solving this further, we need to check whether the solution will exist or not.
00:49
If the solution will exist, then the solution of this system is consistent.
00:55
So for that, we will do the operations.
00:58
First of all, we will swap row 1 and row 3.
01:01
And we get the result as 1, 4, 6, minus 32, 209, 5, 5.
01:12
4 minus 1 3 12 so that we can make a pivot over here in the first row then moving further eliminate the first column that can be done as r2 to be equals to r2 minus 2 times r1 and r3 to be equals to r3 minus 4 times r1 applying this operation we get the result as 1 4 4 6 minus 32 and here we get 0 minus 8 minus 3 59 and here we get 0 minus 17 minus 21 and 140.
02:01
Next what we will do is find the pivot in this column that means over here...