In Exercises 19-26, pivot the system about the circled element: 3 19 20. 2221_22.852 23 212` 532 8324.4 233 [2 25_ 4 0 3 5 6 2 -43526. 032 3_1...

In Exercises $18-23,$ calculate the linear combinations.
$$
\frac{1}{2}(4,-2,8)-\frac{1}{3}\langle 12,3,3\rangle
$$

So the first thing I want to do is write this matrix. So I have one negative tour. Negative 13 for next color, one negative to negative three to name of 35 and for two. So there's my Matrix, and I'm beginning with just based off those acquaintance that we were coming. So my first step has done for me And what that top left quarter to be a one. And it's some to rewrite that first, our first row it exactly the way it iss now. My next thing I want is that next one below it to be a zero. So the way one do that subtract. I'm going to the second room minus the first row. So I have zero four, minus two would be to 13 minus three would be 10 and negative four plus two would be native to second steps done. Your third stuff is I want that night of three to be a zero. So where money that doesn't want to use the top row again. Most play attempts three and added together, so I have zero. Negative. Four was positive. Three is 12 12 plus drives a night of seven, so 13 times TEUs, 26 seven. Negative 20 Sorry, times three. So would be, um it's just right that over here, sincere. I'm not coming for the number. So night of 13 times three was in negative. 39 Should make sure you are getting that so negative 39 plus a four would be me and negative. 30 size, then four times three is 12 plus two is 14. So my next up that's a need. That, too, in the second column to be Is your There started being one. So to do that really first calling alone again for shrew alone again. Then divide the second row by 201 by negative one. Now my next row. I want that negative seven to be a zero. Somebody is my new second row to do that. So if I were dead, multiply that second road times seven on and then add these together so would have zero. One time. Seven. A seven, which gave me zero. Five times seven is 35 which would also get me zero. And then I would have a negative one times seven, which is a negative seven minus the 14. Just seven. So because of this line here No, no, there's actually no solution to these to this set of equations

This way. Even the four times the sixth, minus 11 then minus two times the 10 minus one plus three times the minus 211 And here, the first time I'm going to do with me, I multiply the constant inside. Then again, equal Thio 24 minus 44 and then minus The two is there are minus to plus. Here we have the minus 633 And then the next step, I will do the first component. I add them up together, the first one with minus the second one with a plus. So I have a 24 minus still, uh, minus six. Here, the second one window, second one. So have the minus four minus zero plus three. And the last one, We have the four managements with the plus two plus three. So at the end, we get equal to the, uh this one will be 16 and then we have This will be the minus one. This we have equal to this express three. We nine

So after entering this equations and form of a matrix into my calculator, came up with my final solutions again, the key thing and watches making sure, like on your second equation you don't have a W. So make sure that's placing your major ex zero on. Wash that on all of the equations that you don't have all four variables. So here's the final matrix that I have seven and over 31 6/31 1/31 and 29/31. So this matrix we know that here's my ex value, my wife value my Z value and my w value.

In this question. We argument three equations and our task is to solve simultaneous equations. I recommend the first step to will be to eliminate the denominators by multiplying each fraction by the lowest common fact multiple for each off the equation. So, as you can see after after multiplying, that should be normal fractions in the three equations. And after a bit off cleaning up, we get these three equations. So with these three equations, we can do some manipulation like additional, not all subjection to try to isolate the, um 11 unknown to find its value. And there are many ways you can do this. So there's just one of the ways So I'm gonna self if equations one and two to get to eat immediate why? And then, um, I haven't equation with just X and Z, so I'm gonna do it again with another half equations. So I have two equations that has no why it all just x and Z. So two equations toe unknowns are be able to solve for, um, for X and the so my next there is to eliminate Z to find the value off X. You can do this I know. Way like you can go for excellence rz first, it doesn't really matter. So with the very off X, I can sell it back into high off the to derive equations to find a value off Z. And with the venue off X and Z, you can serve it Bet into any off the three original equations to find the value off by he really doesn't matter which equation you choose. And I chose equation one simply because the coefficients overall looks look smaller. But yeah, like I said, it really doesn't matter. So now we have all three values for X, y and Z. You can also do this with sudden scientific calculators or graphic calculators with simultaneous equation. Solve us. Um, but regardless off which method you use, you should be able to get the same, insists