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If $\left|\begin{array}{cc}2 & -3 \\ p-4 & 2 p-1\end{array}\right|=-6$, then $p=$ (1) $8 / 7$ (2) $7 / 8$ (3) 5 (4) 0

In this problem, we have to find two p managed week. You now to pee wee just multiply every element and p by two. So we get eight six negative or negative to jeer and 10. And then we have minus week. You were wanted by every element. Cue by three. So we had nine 96 minus 15 minus three. I have six and managed three. And then we do the subtraction. We find the first elementary of eight minus nine, which is negative one. And now, before we actually do any other subtractions, we really see the inner answer traces. The only answer traced that has negative one as its best element is each. So we already know that the answers each

In this room. Were given a matrix P. She's a matrix of four or three by three. And elements are even two three zero 57 six eight nine. And the another met sq. Which is equal to 203 three 05 five. Say 10 We have to find group B minus treat you in order to find this to be minus three Q. We will succeed you. Elizabeth. Panic you two and two P. Which is one 06 Right? 258 379 minus three in securities. Two three five zero 07 three 50 Now, we might like to into this Matrix and Money. Three and two. The other way please. So two P. Main street U. Is equal to too much. That I went to 2 to 4 to 36 to 00 To have a 6 12 25 10. To live A 7 14 tom Kloza. 8 16 total our 9 18 minus now. We'll try three. Into the Matrix Resources 2, 1000 031 Close 393 and close 39 See with 5 15, 30037 21 female, 5 15 00 Now, we will support these two matrices to be my street. You when we subject the corresponding and once we get my list for four minus three minus nine, 10 minus one minus three minus five, 18. Yeah. Which is the answer this question. Thank you for what you with you.

For this problem we are first asked to find the general equation of the plane containing the points. P one equals 68 negative too. P two equals four negative 10 and p three equals 100. The way that we do this is by first finding the vector connecting the points P1 and P2 which will be given by 4 -6 in the first component. So negative too, negative one minus eight. In the second component giving negative nine and zero minus negative two in the third component giving us positive too. Then we want the vector connecting points P one mp three which will be one minus six in the first component giving us negative 50 minus eight in the second and zero minus negative two. So positive to in the third then we want to find our normal vector to the plane by taking or finding the determinant of the matrix with I J K along the first row Than P one, P 2 along the second negative to negative nine positive too. And p one P three along the third. So negative five negative eight positive too. So we'll have -9 times two. So that will be negative 18 minus two times negative eight. So it will be plus 16 times I minus -2 times two. So negative four minus two times negative five. So that's going to be minus four plus 10 in the J direction plus -2 Times two. So -4. Or excuse me negative two times negative eight. So that would be double negative. So that's going to give us 16 minus negative nine times negative five. Now that is giving us a triple negative so that is going to be minus and then um five times nine is going to be 45 in the K. Direction. Which we can then when we evaluate this out fully we will get the vector negative two, I minus six. J -29 K. So now that we have the normal vector we can express the general equation of our plane as negative to my cat is on my lap and she just almost fell off. Okay there we go. Uh so would have negative two times X -6 as our first component plus -6. So actually I should write this as -6 times why -8 is the second term? Then we would have minus 29 times zed minus negative two. So zed plus two equals zero as the general equation for our plane. Then for the second part of the problem we are asked to graph this. I've used a graphing software to do the job And this is what a 3D plot of our plane should look like

To solve these we or reduce roar reduced the matrix v Juan Vizio V three p one pizza P three if you're right in the way off. 10 three minus two Soo wan six minus five and they are victory to be 30 solved. Minor seeks on the discipline. Full minus one 15 minus seven minus 53 miners AIDS six 16 miners six Minus its When you wanna worry just days you Oliver 03 equals a row three minus three. Or won't because you want to tone the subzero on then road soon Records overrode soup plus two. One. When you do that, you have won't 000 soo wan zero minus long. 30 30 four minus 131 minus five 37 minus 416 minus 96 Minor. Six. So next thing we do is Dad's we said Erawan equal to because one it's on distant zero equals Aurora warn minus to girl Sue. Under our roof four equals or four plus Soon under you off warn. 000 0100 3010 and they have six minus worn 10 minus 11 37 over. Three minus one, minus 11 6 minus 30 And then lastly, we turned this to zero. So we se ra warn quarter one minus three for three. I said I'll be want 0000100 0010 and then three minus 110 Minus it. Sing 37 over 30 minus one minus 26 minus Terry zero. So this is the this is it in the religious form now, Ralph column for represents p one. So let's let me just write it the gates, right? Remember, this is P one pizza. Ooh, P three. That's what it represents. So we have that. Oh, p one would not be called to three v one minus v tsu plus the three from this column. So because I can write p one in terms of v won't veto a victory, so I'm implies that the one is in. He's you spawn off s. Now, look at pizza pizza. This is not consistent because he's off minus one year where there are zero in all these. So because pizza is not consistent, it implies that pizza ooh is not and spawn of s spawn off s now victory will be spun off is because you have zero here. So we have the eatery you call to minus two V one plus six V two. Monastery Victory. It's implies that Pete three is in Spahn off s. No. If we add the quick, efficient off P one, we are minus three. Sorry. Blustery, actually, since three. Because I'm looking at P 13 minus one plus one. You get three, which is not equal to warn. This implies that P one is not in our fine species off s. Well, if we should add the coefficients off pizza. Ooh, sort of victory. We have minus two plus six minus three. Which is Acosta warn. This implies that Pete 30 is in the are fine space off this.