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(a) 0(b) 2(c) 6Ka)oK Nore U0 uhaakkoe...

Question

(a) 0(b) 2(c) 6Ka)oK Nore U0 uhaakkoe

(a) 0 (b) 2 (c) 6 Ka)o K Nore U0 uhaakkoe



Answers

$$ 6 a^{2} b-2 a b-60 b $$

In BCC, the doctor header the of the avoid it not possible. The couch, the couch in its crystal like this in its digital light taste at the body centered system, body centered cubic system already already BCC at them is was and so no doctor header words are presenting PCC christian so option A. Each correct.

Here we have the Matrix A given by this with the entries negative. 706 05 year old and six zero Number two. And so we have the characteristic equation for this problem can be written as follows Lambda minus five squared times. Lambda plus 10 is equal to zero. So we have that lambda one coming to come on. Three people's five color five common *** 10. So now if we choose Lamb dick them tow one equal to five that we can find the Egan Vector for the first wagon value using the same steps that we did in the previous problems. As given by s time, 010 Where s is a free non zero rial number and Lambda two equals five. So that's the other repeated Aiken value. It's going to give us you two equals as times 102 Thank you. And finally landed. Three equals negative 10. It will give us You three is equal to s times native to zero and one so we can write the general solution as except T is equal to see one eat the five t times you one just given above plus C two times each of the five. T You too. It plus C three each of negative 10 t times you three. And for the sake of being specific, we can take s equal a one off these cases. Since any s works, we can take s equals one to give us the specific version of you on your twin. You three. So we'll have, for example, here you'd have zero 10 And so here we have 102 And so that's our final sleep.

So in the human question we have our metrics, we have a determinant which has given us a four X. S equal to X C zero X C one X plus one C one. In the second group we have two times XC one two times XC two And two times x plus one. See two in the third row we have six times X C two, six times XC three and six times x plus one X plus one C three. So we are told that this determined is equal to F of X. And we are told to find the value of f of 200. Right? So what we can do over here is We can take this determinant and perform a column operation in order to simplify this. Right? So we are going to do a column operation under uh determinant which is C3 changes to C three minus See one Last COO. So then we would have the metrics XC0 is we should know how to take a combination. Right? So a combination of the far N C r is taken us in factorial divided by divided by r factorial times and minus R. Factorial and minus R factorial. So this is how we can find the value of a combination. And the question we have X C zero which would be equal to X factorial divided by let's write it over here. Right? So we can write x C zero would then be equal to X factorial divided by zero factorial times, explained Zero factorial which is X factorial which is equal to one. As for X C one it would be equal to XC one is equal to x factorial Divided by one Factorial Times, X -1 Factorial. Which we can write us x factorial x times x -1 factorial. They wanted by X -1 factory in which is equal to X. And next what we have is X. See express one C one right express one C one which is equal to X plus one factorial divided by X divided by one factorial times X plus one minus one which is ex factory. So this would be equal to X plus one times ex factory and divided by ex factory in ex factory. And it's bacterial councils of. And what we have is X plus one. So similarly we can do uh do this to each combination in the determinant. And after doing the column operation on this determinant, what we would have as the determinant is they would have one XX- Plus one two X X Times X -1 and X plus one times x. Yeah then we have three x times x minus one and we have x times x minus one Times X -2. Right? And x minus X plus one times X Times X -1. So this is what we have, right? So now what we can do is we can take the we can do the column operation now which is C three changes to see three minus C one Plus C two. And since we have simplified the determinant first, by evaluating each combination, we got this determinant. And after the column operation we can write it once more. That is C three changes to see three minus seven plus C two, C three minus C one plus C two. We reject the determinant one X zero one X zero. Then we have two x x times x minus 10 and three x x minus one X times x minus one times x minus one. Explain this to. And here also we have zero. So once we did the column of pressure we got a column inside the metrics which is all zero. Right? So if any one of the row or column in a determinant is all zeros then the value of the determinant would be equal to zero as well. So now we found that the value of the determined given the question given us a four x for fix Is actually equal to zero, which means when we take off of 200, its value will also be equal to zero. So this is how we solve the given question. I hope you understood the mattered. Thank you.

We're being asked to simplify the given expression. Well, to do this, we're going to use the distributive property, so we're going to need to multiply each term inside our prime facie by the mono meal. Negative six A squared B squared and remember to multiply mono meals. You multiply the coefficients. You add the exponents for like basis. So first we're gonna need to multiply. Negative. Six. A squared B squared by five. A squared B eastward. Well, that's going to give us negative 38 to the fourth B to the fourth. Next we'll multiply Negative six. A squared B squared by negative six. Say well, that's contiguous. Pauses of 36 8 to the third B squared. Lastly, we need to multiply negative six a squared B squared by negative six B and that's going to give us pause is of 36 a squared B to the third. And because none of these are like terms, we can't simplify any fervor. So our final answer is negative. 38 to the fourth beat to the fourth plus 36 8 to the third B squared plus 36 a squared B to the third


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