5

0 0 S8 8 828; 0 N 1 (0 (86.3 6.26.16.0 ppm...

Question

0 0 S8 8 828; 0 N 1 (0 (86.3 6.26.16.0 ppm

0 0 S8 8 828; 0 N 1 (0 ( 8 6.3 6.2 6.1 6.0 ppm



Answers

$$\left|\begin{array}{rrrr} 0 & -3 & 8 & 2 \\ 8 & 1 & -1 & 6 \\ -4 & 6 & 0 & 9 \\ -7 & 0 & 0 & 14 \end{array}\right|$$

So we have 73.2 parts per million. Which by definition is going to be 73.2 g of whatever salt over a million or 10 to the sixth grams total. Um so we need to just simplify this to get grams over grams and then multiplied by 100% and we'll get our weight percent. So this simplifies to 73 two And then times 10 squared divided by 10 to the sixth is basically saying times 10 to the negative four. And then we want to make this a number between one and 10. We make it smaller to make that one bigger. So it's going to be 7.32 time soon To the negative 3rd percent by weight.

So in this problem, we're given this matrix and were asked to use the matrix capability of a graphing utility to find the determinant. So I went to Desmond's dot com, went up here to math tools, matrix calculator, and got this matrix calculator here. So in our new matrix and our matrix is a four by four. So four rose and four columns. Now the entries one minus one, C A A and four and two and six zero my S four and then to zero two and six and then zero two, eight zero. Okay, where's my matrix now? Just do D E T right here to get the determinant determinant of a yes, Negative,

Let's divide 11 and seven hundreds by six types. So in order to do this using long division are divisor on. The outside needs to be a whole number, and right now it's the desk bolts your plants. It's so we could move the decimal point over one place value to the right. If we do that, we must do the same thing to our dividend on the ends up. So we move it one place to the right. Now we have six on the outside or divisor and 110 point stuff. All we did was multiply both of these by 10 which will give us the same answer. So now we're gonna bring our decimal point straight up. We're going to start dividing six goes into a one. It does not. Six goes into 11 one type one time. 66 subtract 11 minus six is by. Bring down our zero six goes into 50 eight times eight times six is 48. Subtract. You get to bring down ourselves. Six goes into 27 about four times four times six is 24 27 minus 24 is three. We don't have a zero remainder, but we have no more numbers to bring down. So we're gonna add a zero and bring it down. Six goes into 30 evenly. Five times five times six is 30. When we subtract, we get zero as a remainder. So are quotient is 18 and 45 adverts.

In this video, we're gonna go through the answer to question number five from chapter 9.5 were asked to find the values and I can vectors off the matrix A So first find I'm values. Let's find Determine off the vector. Sorry of the matrix. A minus I This is they made at the determinant off bomb minus R zero. They were zero minus, uh, two 02 minus, huh? So expanded over the top row. We've got one minus our sides by the territory, Right, two by two matrix, Which is Ah, squares minus four. So if we set that equal to Zoomer on and by the bracket on the left is equal zero, which gives us, uh, is equal to one or the back on the right sequence zero, which is Either I was equal to minus two or two. So there I am values for this matrix. Find corresponding Aiken vectors. That's first. Look at the Eiken vector. Corresponding. Talking about you one. So we've got a minus one times didn't see matrix times. What? We're going to find the Eiken vector you want. This is gonna be a zero 00 too restricting Born from the leading Dagenham zero minus one, two zero, two Minds well, times you want is equal to savor. So from this, we can easily see that the second or third components gonna be zero. Because they're the only values of the second component of you one and such that these guys both satisfied on that leaves us with just an arbitrary value for the first component. So we can just set it up. Next, the Eiken vector associated with the hidden value. Yeah, I was equal to minus two. So got a month's arse. That's a plus. Two times the identity matrix. I times you on equal saver. So it's gonna be 30 There are 0 to 2 02 two you won't is equal to zero. Therefore you want could be equal to Well, the first component is easy because it's just three because this first row with the Matrix tells us that three times with the component of you is equal to zero. Therefore, that's important. Speaking today right on both of these to tell us that the second circle bonus just the next reach of that. So we set the meet. I want to be people to one, then the Bob. So that's our second dragon vector. Our third I come back to disassociated. The value are people too, so that Ah a minus Thio I is equal to zero. It was that should be a yuan in there. This implies that minus one zero They were zero minus one too. Zero two minus one. What time do you want the Xaver? Excuse me? This middle one should be minus two and they should be minus two as well. Because the Eiken vector. That's because the Eiken value is to therefore you want Thea Aiken. Vector is gonna pay. What? The first component CT. So determined It's just gonna be zero. That servant from the equation from this, uh, from this world matrix on these rows of the Matrix tell us that the second and third components off the item vector the same as each other. So we set the middle. Wanted one, but the bottom or phone and that's on file.


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