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[ The conhaence Mlenle 1 Homework: 11 (7s 1 Ch 10 SecLu /I 1...

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[ The conhaence Mlenle 1 Homework: 11 (7s 1 Ch 10 SecLu /I 1

[ The conhaence Mlenle 1 Homework: 11 (7s 1 Ch 10 Sec Lu / I 1



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$$\text {In Exercises } 11-18, A=\left|\begin{array}{rrr} 1 & -2 & 3 \\ 4 & 5 & -6 \\ -7 & 8 & 9 \end{array}\right| . \text { Find each minor or cofactor. }$$
$$M_{13}$$

So here we have Matrix A and we are asked to find CO Factor 13 or C 13. So first, let's add the I and the Jays together. So we have one plus three equals four because four is an even number C 13 or the co factor 13 is simply the same as the minor 13 or M 13. So that means all we have to do is find M 13. We can find m 13 by deleting one and a leading column three. So we end up with four native 75 eight within multiplied diagonally. So we have a Let me with that. We have four times eight minus five times negative seven. So we have 32 my ass. Negative 35. We add the two and we end up with 67. So C 13 is the same as M 13 and they both have a value of 67

So here we have this matrix A and we asked to find M 21 or a minor 21. In order, find the minor. We must delete the rows and columns that are given to us. So the two here tells us that we must elite row too. So we delete all of this and the one here tells us that we must delete. Call it one. Now the minor is simply the elements that are left or native to a 39 And we can easily find the determined of this. So it's simply native two times nine by us to be times it. So we have native 18 my ass 24. So we add the two together. So negative 18 by eso 24. So we get negative 42 as this minor

We're being asked to simplify the given power by. Well we have one divided by one over. Or sorry one divided by I. To the -11. Remember when we were dealing with exponents we never want our exponent to be negative. So to make it positive we're going to move this to the numerator. So that means we really just have I to the electric power. Now we can try and simplify remember our powers of I follow a pattern where I to the first is equal to I. I square this negative one. I. To the third is negative. I And I to the 4th is equal to one. And remember then our pattern would start over again. So every fourth power of I we start over so we begin by figure out. Well how many times does four go into 11? What goes in two times with three left over. So we can rewrite this as I to the fore being squared Times I. To the 3rd. Well we know that I to the fourth is equal to one, so we have one squared and I to the third is negative. I, Well one square is one and one times negative I is negative. I perfect. We now have our simplified answer. It's negative I.

So here we have a matrix A and we are asked to find a co factors. See 21 for this matrix. So first, let's add the I and J together. So here's I and here's Jay. So we have to plus one equals three because three is in our number. C 21 equals negative M 21. So we would find minor M 21 then just negated to find the co fact of C 21. So let's find I'm 21. M 21 tells us that we must delete Row two and call him one. So we're left with negative to eight 39 So let's find the determinant. We have negative two times nine minus three times eight. So get negative 18 minus 24 and we subtracted. Teoh are add them when we get negative. 42. Now that's the minor. So if we want to find the co fact that we would simply have to negate this so the co factor equals positive. 42


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