a-2-times-200-data-matrix-d-contains-the-coordinates-of-200-points-compute-the-number-of-multiplicat

Question

A $2 	imes 200$ data matrix $D$ contains the coordinates of 200 points. Compute the number of multiplications required to transform these points using two arbitrary $2 	imes 2$ matrices $A$ and $B$ . Consider the two possibilities $A(B D)$ and $(A B) D .$ Discuss the implications of your results for computer graphics calculations.

Runpeng Li · Accepted Answer

get. So in this problem, we present you to find the changeup Coordinate matrix from you did see so you to the scene. And this will be this can be achieved by first food. The column vectors of be on right heart, its matrix seven nectar to two active one and column column vectors of sea or one. And why two? So the way to do that we do the, um, reduction. So we first divided first roll by poor 5/4 7/4 and to quitters. And second of all, would still be one too negative. Two and one next one. Okay, so this gives. So we used the second row diva minus the first roll. We have you to minus 4/4. That is 3/4 and 7/4 minus 7/4 minus two. That is 1/4. Well, yes. So he&#x27;s actually we used one minus one and two minus five over four. That&#x27;s 3/4. And next to minus 7/4. That is negative. 15 over four. Right, Because selective to minus. Just for 60 minus 7/4 that&#x27;s Ah, eight rito plus seven. I could sit 15 over four. Yeah, and the last one is 91 minus two or four. So that is. See, um, keep six. 04 And we still have the first roll. Libel before seven over four and tour. Okay, now we first to turn the second row. We multiply second row by for over three so we can turn this entry to be one. So we have a life. Local traitors, 7/4 two porters and 01 and three over four. Yeah, it&#x27;s one and or third times negative. 15. What? Hers that is 5 95 and negative. Six or four times where? Oh, where Three. That is connected to. Okay, So for the first rule, look, I use 5/4 off the second reel ad. First role. Sorry. Minus first, So we can cancel the entry of the entry here. So that&#x27;s 10 and 544 times negative. Five used. Seven over four minus is value. So it&#x27;s seven over four plus 25. She&#x27;s 32 or four. So that&#x27;s eight. And we also have to over four. Finest. I&#x27;m over four times negative too. So that is 10 plus two or four. So that&#x27;s three. We have three here. 01 and active, applied negative too. So I were change. According the Matrix from B to C is eight three negative five and negative too. And the inverse C two B. It&#x27;s the inverse off the you to see and remember how we find it. Find the inverse up two by two matrix First the best A determinant. Uh, this matrix, which is? Uh um you to see times we have the changes have to entertain you The diagnosis that selective too. And eight No, we have to take the negative 23 And what? So what&#x27;s the determinant determined then? Days negative 16 plus 15. That&#x27;s negative one. So multiply by multiplied by wants us to read negative five and activate.

Ankit Gupta · Answer

here we are given with men. Traces a off the order to cross tree. Be with the order to close three c off the order three close to nd off the order to grow stool. And we need to find a plus two seats. So is off. The order to close tree and see will be off the order three Grosso Hence we can observe. So to see will also be off the same order three close to so only men traces off. Save order can be added my braces off. Same order can be added hands We can say that a plus to see is not different.

Ankit Gupta · Answer

in discussion v are given to determine whether we have the weather This operation see multiplied with a place to be. It&#x27;s possible or not. We can also that the metrics is off. The order to cross three and metrics to be is also of the order to cross three hands. Buddha mattresses are off these same order and we know that only mattresses off. Same order can be added or subtracted. And as Buddha mattresses are off, same order hence a plus two. B has dimensions. Gross three. Now let&#x27;s take for see this metrics See is off the order three cross to and we can observe that number of columns in metric C is equal to number off rules. In my tricks, a place to be hands the operation see multiplied with a place to be it&#x27;s possible and the metrics semen replied with a place to be will have dimensions. Three grows three, which is given by a number off rules in C and a number of columns in a pless to be thank you

Ankit Gupta · Answer

in discussion of we have to determine whether the Operation CD minus D it&#x27;s possible or not. So the oppression see is the geometric see off the dimension three cross to and metrics be off the dimension to cross tree and we can Also that number off columns in C is equal to a number of rules in be hence, the operation CB is possible and our metrics CB well off the order three course three. At the same time, we have dramatics d which is off the order to cross to. And we know that if you want to add or subtract to make races, only my braces off, same order can be subtracted or added hence we can arm so that when this tumor traces off different orders, then these operation that is the operation off subtraction is not possible.

Ankit Gupta · Answer

in discussion of any toe determine whether the oppression CE minus deace possible or not, we are given with a as to cross tree bs to cross three. CS three close to nds three to close. So let&#x27;s first identify for C A. We have the metrics e with order three close to and Matic save in order to cross three so we can observe that the number of columns in C is equal to number of rows in a Hence the operation. See it&#x27;s possible and see a will be off the order three. Cross three that is number of frozen sea and number of columns in a Now we have d off the order too close to and we have to perform the oppression ce minus t which is not possible because only mattresses off same order can be added or subtracted. Subtraction is a negative edition, so it is not defined or not possible. This operation is not possible

Problem

Consider the following geometric 2 $\mathrm{D}$ t…

Problem 9 Easy Difficulty

Answer

since (AB) D requires almost half number of multiplications it will be preferred for computer applications. For a larger data size this difference will become more significant.

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

Linear Algebra and Its Applications

Grace H.

Heather Z.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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since (AB) D requires almost half number of multiplications it will be preferred for computer applications. For a larger data size this difference will become more significant.

Linear Algebra and Its Applications

Grace H.

Heather Z.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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

Grace H.

Heather Z.

Kayleah T.

Caleb E.

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

Linear Algebra and Its Applications