5

32331-2-3...

Question

32331-2-3

3 2 3 3 1 -2 -3



Answers

$$\left[\begin{array}{ll} 3 & 2 \\ 3 & 3 \end{array}\right]\left[\begin{array}{rr} 1 & -\frac{2}{3} \\ -1 & 1 \end{array}\right]$$

Okay. In order to figure this out in the desert, a scientific calculator. We're going to start with the base, which is 13. And then to get an exponents, I'm gonna quit eight to the beef power. And that lets me pick any exponents. My exponent is five 13 to the fifth. Power is 371,293.

To graft the line f of X equals 1/3 x minus two. I'll start by making a table of values and then I'll plot the points. So if x zero f of x is 1/3 time zero minus two, which is negative too. If X is three f of x is 1/3 times three minus two, which is one minus two or negative one. And if X is negative, three f of X is 1/3 times negative three minus two, which is negative. Three. Now to plot the points. Zero negative, too. Three negative one and negative three negative three and then we'll connect those points and extend beyond them and we have our lying.

To solve this problem, I'm going to use penned ass. So first I'm gonna look for a parentheses. Then I'm gonna look for exponents than multiplication and division in order from left to right, the addition and subtraction. So when I first scan through, I noticed I don't have any parentheses. I don't have any exponents. Now, I'm gonna look for a multiplication or division. And so the first thing that I see is I've got 3/4 times, 1/6. So this is the kind of thing that, if you can't do it in your head, would be really good to do after the side somewhere so you don't clog up your work. So over here I'm gonna do 3/4 times 1/6. Now, one way to multiply fractions is just a multiply straight across. So three times one is 36 times four is 24. But then I would see they both have a common factor of three. And so my final answer would be one ace. Or you could remember You could see at the start when you're multiplying. These that three and six both have a common factor of three, so you could divide three by three is 16 by three is to now you could multiply across one times one is 14 times two is eight. Either way is fine. As always, you remember to reduce your fraction. So I've got 3/4 times. 16 was 1/8 plus about the same time. You could take more than one step if you wanted, but at the same time, you could multiply 1/2 by 1/3 because, you know, the multiplication is gonna happen before the addition. So again, you could do that over here, 1/2 times 1/3 if you multiply across one times one is one, two times 36 and you're gonna get 1/6. Now, in order to add fractions, you need a common denominator. And so that means that I need to find a number that I can change both eight and 62 by multiplication, preferably the lowest until the lowest one that I can think of is 24. And so to change 8 to 24 I would multiply by three. But whatever I do, the bottom have to the top. So 1/8 would become 3 24th and then six changing to 24th would be times four, and I also did it to the top. So that would become 4 24th And then to add fractions, you keep your denominator and add your numerator three plus 47 so 7 24th

Okay, This problem, we have equals to falling. And it's also a three by tweet matrix. So we have negative. 310 and then zero negative. 31 and four Negative. Eight two. Now we can obtain the characteristic equation again. As follows. The same exact procedure as the previous problems. We have a negative Lambda cute minus four. Lambda squared minus five. Lambda minus two equals zero. So, Landau, one comma to come on three are gonna equal native one negative one. And negative, too. Now, for Lambda equals negative too. We want to solve the following equation for the Eiken victor. A plus two i times u equals zero. Then we'll obtain u equals T where Ty's every parameter, as always, times 111 And for Lambda equals negative one. We saw this equation a plus. I times you equal zero. And when we solve this, we will get you is equal to a T times 1/2 1 and two or equivalently team times one, two and four. Because this is just the Eiken victor skilled differently, scaled up. And so we have our answers


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