use-partitioned-matrix-multiplication-to-compute-the-following-matrix-product-which-appears-in-the-a

Question

Use partitioned matrix multiplication to compute the following matrix product, which appears in the alternative formula (5) for a Bézier curve:
$\left[\begin{array}{rrrr}{1} & {0} & {0} & {0} \ {-3} & {3} & {0} & {0} \ {3} & {-6} & {3} & {0} \ {-1} & {3} & {-3} & {1}\end{array}ight]\left[\begin{array}{l}{\mathbf{p}_{0}} \ {\mathbf{p}_{1}} \ {\mathbf{p}_{2}} \ {\mathbf{p}_{3}}\end{array}ight]$

Ankit Gupta · Accepted Answer

So here we have a five cross five metrics. In order to get the determinant off this I prefer expanding along this column toe soil rewriting two times before crossword metrics that will be off tenders minus toe. 163 Okay, 10 to 5. Basically, I&#x27;m diluting this row and this column. So 34 minus 11 and finally and have 2000 So this is a four crossword metrics again to expand this for cross for metrics and prefer expanding along this column for so two window here plus minus. This tool will commit a negative sign. All right, so that is important. So I have to mention this as minus two. Then again, I&#x27;ll expand along this. So this is plus minus plus minus. So again, on minus two. And now I lover three across three metrics. So that is 163 0 to 5. And this is before minus one and one. So this is where you come. Sort Toby for Molly Blair. Way One indoor the window Do plus 5 37 onda plus minus plus. So that this? Plus four times 65 30 minus six. So there s 24. So this value comes out to be but again condition. So, as I can see, this value comes out a week for one toe. So that is the value of the determinant of this given metrics.

Elham Kordzadeh · Answer

you have? The motorist Minus seeks nine minus. Why? One nine minus lawn minus. Ploy to minus. Going minus. Climb nine minus three one to minus three one. Once you build boy in other countries, The cheese. It was a little point for you. Who on bon minus flybe to one to to me point. Well, I never. For uber point five number one 0.5 three point, I&#x27;ve slipping to win point. Why? To 5.5 20.5 till any flight. The result would be a trick. We cheesed this little point line zero Siegel Siegel, Tzeitel 0.5 zero Tzeitel. His legal Riedel Tzeitel point fine is legal. Tzeitel, Tzeitel, his little Tzeitel point flight.

Ankit Gupta · Answer

in order to get the determinant of this matrix, I prefer expanding along this first column. So I will be writing minus one into this is three into three. So that this nine miners zero, let it. Then when I write with a negative sign zero whatever it is coming that will visit only plus zero into something that will also be zeros. Effectively, this will be minus name. So that is my answer.

Ankit Gupta · Answer

So, in order to evaluate the determinant off this five cross five metrics on prefer expanding along this first column. So rewriting five in tow before cross for metrics. So that this 1432 000 263 three for one and 00 toe. Although the elemental way zero as we know. So this one I can expend once again along the first all of itself. So that will be five in tow, one in tow. A tree grows three metrics So that just 263 34100 toe So I can see that I will expand this along. This car drove so that will give me less. Minus, plus minus Plus. So five in Toto. This will be so for the eight minus 36 18. So that value comes auto with 10 in tow. My understand. So this is a quarto minus 100. So that is my answer

Vishal Parmar · Answer

This is our question Number 28. Well, you&#x27;re we have 30 right? So try to make Syria or here, right? So our appropriations would be all right. Do Minus three times all three. Right, So we can make zero over here. Score New Met. Makes these your first tar fourth and fifth through our entities. No. Here. The second row is, uh, double Dio minus 91 and you&#x27;re negative trend. Right? But we can find the determinant off the metrics using the second call. Oh, right. And here we have one. Right, But the sign off second element should be here. Negative, right, Tool? You&#x27;re retired too, right? Never 81 times. Or for my four metrics bees. This is our first problem. And these are the three Poland, right? And we need to eliminate the third federal. So are four by four magics. Ease. Do minus one threes. Easel. You&#x27;re zero minus 91 No, I gotta drain one warm minus 10 And here, treat toe. 05 Right. No. Try to make zero. Or here and your right. No, for the first row or rope. Grecian is our one minus two times are three and for here Our operation is are for minus three times are three. So our new for my format leaks is year zero minus three. If I see you. Zero minus 91 and my understand you&#x27;re tired. Ruiz. Aditi&#x27;s and the forgeries zero minus one. De and five, right? No. Find a determinant off the metrics using the first column. Right. So here, be easy, quarto Minus more times. No. Eliminate your first column and wardrobe. So are to buy three medics. These negative three by zero. You&#x27;re minus 91 and negative trend. And here we have negative one tree and five. No wonder determinant off the metrics using the first rule. You&#x27;re five or EUR five. Multi by they want. That is fine on the negative. Drain money by by three. That is 30. You&#x27;re We have negative fire. Five months by my negative nine. That is 45 minus your 10. Multiply by one that is done. And here we have zero already for the easy part, minus one time. Authorities must fight that he&#x27;s 35 and 45 plus 10. That is negative. 55. So here the is equal to minus one. 35 Mother. My very negative do that. It&#x27;s 105 plus here to 75. So the determinant automatics least negative. 1 70 Thank you.

Problem 18 Easy Difficulty

Answer

$\left[\begin{array}{ccc}{1-3(1-s)} & {3(1-s)^{2}} & {-(1-s)^{3}}\end{array}\right]\left[\begin{array}{c}{\mathbf{p}_{0}} \\ {\mathbf{p}_{2}} \\ {\mathbf{p}_{2}} \\ {\mathbf{p}_{3}}\end{array}\right]$

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Linear Algebra and Its Applications

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$\left[\begin{array}{ccc}{1-3(1-s)} & {3(1-s)^{2}} & {-(1-s)^{3}}\end{array}\right]\left[\begin{array}{c}{\mathbf{p}_{0}} \\ {\mathbf{p}_{2}} \\ {\mathbf{p}_{2}} \\ {\mathbf{p}_{3}}\end{array}\right]$

Linear Algebra and Its Applications

Anna Marie V.

Heather Z.

Kristen K.

Joseph L.

Vectors Intro

Vector Basics - Example 1

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

Anna Marie V.

Heather Z.

Kristen K.

Joseph L.

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

Linear Algebra and Its Applications