5

IctAL ;, 0 0 9,c-|1 compute 4+N 6 BC det(AB)"...

Question

IctAL ;, 0 0 9,c-|1 compute 4+N 6 BC det(AB)"

Ict AL ;, 0 0 9,c-|1 compute 4+N 6 BC det(AB)"



Answers

Calculate the determinant
$$\left|\begin{array}{lll}
a & 0 & 0 \\
0 & b & 0 \\
0 & 0 & c
\end{array}\right|$$

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 here we are given that the matrix is equal to three minus two six and four. So we need to find out what is the end N. Was equal. So yeah it was his equal to one by determinant of this matrix that is three and the 4 12 -6-2. That if plus 12 Indo will interchange the difficult element that is four and three and will change the sign of the other elements. That is negative six. And So this is going to one x 24". Or we can directly right a desk four x 24, two x 24, -6 x 24 And three x 24. So this is the cosmetics which is equal to one by six, one by 12 -1 x four and one by eight. This is endless. No we need to find out what is Yeah. Yeah it was that is or a three minus two, six and four window. Our main was that is one x 6, one by 12 -1 x four and one by so this is equal to and dying. Matrix multiplication. We get that is indicated as the entity metrics.

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.

We want to get the fundamental mattress off the system. Exodus shifty equals the method X a multiplied by X 50 and we are allowed to use a computer software to calculate the Egan varies on the Yangon victors of the metrics. By using a software we can get that the island values of the metrics or equals post minus one. These are real Eigen values, and we have complex values where r equals who plus three i two plus or minus three I and these are the complex. I am values we can get from this complice Eikenberry that all four equals two real bird and B equals three, which is a compression of the imaginable. And using a software we can get the again. Victor's corresponding to each Eigen value at r equals one. They have Eigen Vector you equals 1111 one on one and at R equals minus one, we have the again Victor one minus one, one minus one. And for the complex again, Victor Eigen values R equals two less Really. For example, we can get that equals one two plus three I minus five plus 12 oy minus 46. Last night and I and we can spirit the report and the complex port. The report is one Tu minus five, minus 46. And the measure Bert 03 12. And my and we call this Victor A. And this Voeckler is called the That We can move on to get therefore solutions of the system. Where except one of t equals see one. But the boy boy eat is about are we start by the real constant. We start by the Rinne Eigen values. We have the first Eikenberry one. It was about a rt. We have our one Then It's either a lot of tea but the blood by the victor you which was 1111 The second solution equals C two e. There's a lot of rt we have now are equals minus one. This is minus t live by the victor You To which waas one minus one one minus one. No, we get Take a three off the using oil This formula C 31 tabloid boy, cause I in first we have it was about of all Fatih as we remember that we have alpha equals two is alpha and beta a called history we have It was about all 40 duty, but the blood by cruise line May 30. We have better three while the boy was a victor A that we have e one to minus five minus 46 plus no. These mines minus. He was about of all 30 science May 30 the blood by the victor being now we have the 03 12 9 and similarly we can get next four equals C four multiplied boy the same as its three Andriy Switch designs on science and switch The sign in between We have either or to t sign three t to blow by the victory one to minus five minus 46. Plus, he was about off duty cause I in pretty buoyed by the victor B 03 12 line. Now we can get the fundamental metrics. We have four victors. The first victor's comes the first victor come from X one the second x two and so on. Then we have the fundamental metrics x off the equals. It was about of tea. Either a lot of the either or tea. It's raw. 50 from X one from X to eat is about off minus T minus. It is about a dynasty, each of our finest e minus eaters or by S T. And the third victor is it is about off duty design three D, then minus five. It is about of two. T Resign three D minus. It is a lot of two. D minus three is about to tee Sign three t Andi, No, look, look minus that. Said who He's not minus five is to. And the third a number. The third element is minus five. It was about of two t cause I three t minus 12 eaters about turkey sign three D finally, minus 46. Eats about off duty cause I three D minus mine. Neither were off duty Sign Pretty. And the fourth victor is it is a lot of duty Sign three d. We can switch the science and resigns And the sign in between for this vector for easier Caucasians, Then we have to. It was a lot of duty saying 70 plus three years or 30 cause I in three D and we have minus 5 ft to the world of two. T sign, sweetie Plus will. It was a lot of duty cosigned three t and finally we have minus 46 a drawer off duty, cause I in three d bliss nine. It's a lot of two t cause I in three D, and this is a final answer off our program.


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