repeat-exercise-7-when-mathbfv_1leftbeginarrayr1-0-3-2endarrayright-quad-mathbfv_2leftbeginarrayr2-1

Question

Repeat Exercise 7 when
$$\mathbf{v}_{1}=\left[\begin{array}{r}{1} \ {0} \ {3} \ {-2}\end{array}ight], \quad \mathbf{v}_{2}=\left[\begin{array}{r}{2} \ {1} \ {6} \ {-5}\end{array}ight], \quad \mathbf{v}_{3}=\left[\begin{array}{r}{3} \ {0} \ {12} \ {-6}\end{array}ight]$$
$$\mathbf{p}_{1}=\left[\begin{array}{r}{4} \ {-1} \ {15} \ {-7}\end{array}ight], \quad \mathbf{p}_{2}=\left[\begin{array}{r}{-5} \ {3} \ {-8} \ {-6}\end{array}ight], \quad 	ext { and } \quad \mathbf{p}_{3}=\left[\begin{array}{r}{1} \ {6} \ {-6} \ {-8}\end{array}ight]$$

Gideon Idumah · Accepted Answer

to solve these we or reduce roar reduced the matrix v Juan Vizio V three p one pizza P three if you&#x27;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&#x27;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&#x27;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&#x27;s we said Erawan equal to because one it&#x27;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&#x27;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&#x27;s let me just write it the gates, right? Remember, this is P one pizza. Ooh, P three. That&#x27;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&#x27;t veto a victory, so I&#x27;m implies that the one is in. He&#x27;s you spawn off s. Now, look at pizza pizza. This is not consistent because he&#x27;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&#x27;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&#x27;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.

Viswesh Uppalapati · Answer

in this video, we&#x27;re gonna be solving problem number 28 of section 3.3. It asked. Says, um, so we&#x27;re given, uh, two vectors that form a parallelogram and a, um, end of matrix A that maps that poached parallelogram in a linear transformation. Um, from X to X. So we&#x27;re told to, uh, we&#x27;re told to find the area of the parallelogram and the area of the transformation so they find the area. The parallelogram is simple. Here in part. A, um we just used term nine, which states that the area of parallelogram is just, ah, the determinant of the matrix that is formed by its, um bye bye. The vectors that created and were given the two vectors like to create the parallelogram B one and B two. So it would simply be, um, Dobson, Value of the determinant of 401 of seven and one, which is equal to the absolute value of four times one minus seven are negative seven times zero. I was just, uh, just for because negative sometimes 00 So is just for and part be to find the area of the ah transformation. We used to room 10 which states that, um, which states that the area of the of the mapping is just gonna be the area of the parallelogram created by that mapping. So which we already found here, which is for so be the formula would be determined to be, in this case, times the area of a which is equal to four times we used him nine again, which is just the determinant of five. Two. Sorry, No, supposed be a 535211 was equal to four times the upset value of five times one minus two times one is equal to four times three was equal to 12. So these were two answers to the two points.

Liuxi Sun · Answer

so to multiply these makes fractions, We&#x27;re gonna try to turn them into improper fractions first, and do that we multiply each number by the denominator. So two times five is 10 at the numerator is 11 and we&#x27;re gonna keep the same denominator times four times seven is 28 plus three is 31. This gives us we&#x27;re gonna multiply the denominator and numerator separately and 30 11 times 31 11 times 31 is equal to 341. So you can leave it in this form as an improper fraction. Or we can turn it into a, uh, mixed reaction by noticing got 35 times 10 is 350 which is slightly greater than 3 41 So using nine over here and 35 times nine is equal to 315 and 3 41 minus 3 15 So the remainder is 26 26/35. So nine and 26 7 35 is the mixed fraction version of the answer

Brandon Fox · Answer

um to 14 goes into 5 77 twice to 14 times two is four 28 Lewis of Tracks, 5 77 minus 4 28 We get 1 49 dropped to seven down now to 14. Goes into 14. 97. Six times Almost seven six times to 14 is going to be 12 80 four. And so 14 97 minus 12 84. It&#x27;s 2 13 so we have the answer of 26 remainder 2 13

James Chok · Answer

Okay, so we want to find our hyper claim that separates p between the one return B three. So when the graft these points in this graph we&#x27;ve noticed at the side of the tribal closest to pee is this be three months being one. So we want to find a perpendicular we want. We want to find the vector perpendicular to the B three miles. Be one line. So to do that, we go be three Whoa, Yeah, B three minds by V. One is equal to four month&#x27;s one gives you three for my security too. So then the line have been declared to this line B three Maestro V one is it 23 and one pass by two and two, which is equal to zero. So solving for in one you have in one is it going to minus two and shoot over three? So then we said n two is equal to three and n one is equal to minus two. So a perpendicular victor is in mine institute and three again. Now a linear functional then is very simply as a function off exper is equal to minus two x one plus by three x two. So now what? What this equation governs is governed lines which go in this direction. So maybe I was brought out government line that goes in this direction parallel to V one and V two. So what we want to serve you wanna be free. So what we want to do is that we want to find which of these lions are possible to fit between P and B three. So what we do is we substitute F O V one and we find that his mind is to test was tough to tell. No one is mice too, just three times to give you six. So that&#x27;s four and you also find out that the two is also equal working status works that minus two times but five is 10 plus three times one appointment operation. It&#x27;s like this so as a function of these three because the fees on this line is equal to minus two times for which admires eight plus three times, for which is three times for which is 12. So that&#x27;s equal to four and F. O. P. Is equal to two times my minus two is minus four plus St Century which is nine. So this is equal to buy. So what this tells us is that to be on this exact line, we need D to be beautiful. And then to be on this exact like to be on this exact line that passed Point p. You needed to be five so d is able to buy. And to pass along this line, you need D to be full, so it should be anywhere in between, or you simply need is you need for to be less than the less than five also in light that there&#x27;s no there&#x27;s no equality because we want them to be in between, not on lines.

Samuel Ewusi Dadzie · Answer

we are subtracted two makes fractions and before we do, we do that. The festivity to do is to make sure the nominee this year then here are equal in this case, the energy core. So we need to fix that, and I will use the notes down here to fix that problem. So I have seven of 12 minus five over six. Now I will find the least common multiple off the gymnasium 12 and six. Even before that, seven of 12 is coming from this side, and then favor by six is coming from that side. Okay, now in the least common. What&#x27;s both 12 and six? Just war. So I right, it&#x27;s here. 12 divided by 12. It&#x27;s 11 time 77. It&#x27;s a minus sign and then 12 divided by six is two to tens. Five s 10. Then, on this point, I was split the result. I hoped in here into this seven of the 12 ago in first of over 12 and then 10/12 green for favor. Six. That will rewrite the question. Eyes this because the Tunisia equal can subtract the whole numbers and every kind. Subtract the memories. But we have a problem here When you subtract two from fight to from seven have a positive onasa but I want to subtract them from seven. Have a negative answer. So what we have to do here is to have toe you right? This makes fraction so that we will have the new media here to be bigger than the numerator here. And I will usually note to fix that issue here. So I have this and every sequel to this. Then I will brew one from a seven and I just do this fraction I can be right one US toe over toward because the two new Malaysia equal I can add enumerators and divide by the quantum leader sued 12 plus seven is 19 in divided by 12. Then this is equal to that&#x27;s So this makes faction will come and replace this, um extraction. Then the animal is here are equal so I can subtract the who numbers and noticed that this new era is bigger at this marina now six minutes six minutes to its full 19 minus 10. It&#x27;s nine unidentified by the common denominator, which is 12. This is correct, But a nudist you can&#x27;t simplify this answer. Three kind divide and I m three kind of ICT walk. So the finalist issued with this four whole number Now? No. Now, when NY divide when three device nine. The resort is three and three. Device to of the results is for so the finances should before who number 3/4.

Problem

Suppose that the solutions of an equation $A \mat…

Problem 8 Medium Difficulty

Answer

$p_{1}, p_{3} \in \operatorname{Span} S$
$p_{3} \in \operatorname{aff} S$

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Caleb E.

Samuel H.

Michael J.

Joseph L.

Vectors Intro

Vector Basics - Example 1

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$p_{1}, p_{3} \in \operatorname{Span} S$$p_{3} \in \operatorname{aff} S$

Linear Algebra and Its Applications

Caleb E.

Samuel H.

Michael J.

Joseph L.

Vectors Intro

Vector Basics - Example 1

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Caleb E.

Samuel H.

Michael J.

Joseph L.

$p_{1}, p_{3} \in \operatorname{Span} S$
$p_{3} \in \operatorname{aff} S$

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications