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Question

Use matrix multiplication to find the image of the triangle with data matrix $D=\left[\begin{array}{ccc}{5} & {2} & {4} \ {0} & {2} & {3}\end{array}ight]$ under the transformation that reflects points through the $y$ -axis. Sketch both the original triangle and its image.

Gideon Idumah · Accepted Answer

Okay, So to answer this question, we states that&#x27;s the metrics off. The transformation that reflects points through the White House is the wife of disease. He&#x27;s a equal to minus 1001 That is, your Tunde. You are a minus one to the ex exist. That is the matrix of transformation that reflects points to the white exists. So this implies that&#x27;s the transformed did some metrics is a mord implied by D because we are told to find the image off the triangle on the the MICEX d. So you do eight times D, which is minus 1001 more supplied by five sue for zero Sue three. Andi transformed mattress These minus 50 minus to do minus four on three. Now we&#x27;re told toe sketchbook. The original triangle on its image says, Dude, that&#x27;s we have something like these. I&#x27;ll just make a sketch here and then we have Let&#x27;s see. 12345 Oh, need one, Sue three. Let&#x27;s end it for So this is X to this is eggs one. So the original image is the original triangle is 5 to 4 sorted there, so I have 50 rights. So that&#x27;s the exes. Five The Y zero. That&#x27;s five. This is one soon 34 fire. So this would be five comma zero. The next one is true. Commit Suso X one is two extras to Dar was somewhere here on the next one is X one is four Extras three. So that&#x27;s four for my three. I was somewhere here and we have this. So this is this. You can just shoot that in Now. The other one is transformed. Image is minus five, comma zero signing to making minus five years. I&#x27;ll be 12345 So I have minus find common zero sadistic beads. X one is minus five. Have minus to commit Su Don&#x27;t be here. And an arm minus four, comma three. So this is minus for under three would be somewhere here. So the image, I guess he&#x27;s This are my over gun sketch this world. Okay, so something like this. So Don sits

Erin Kirchmeier · Answer

in this problem were given the coordinates of the Vergis ease of a triangle in the coordinate plain. And we are out to find the images of these Vergis ease through this transformation. Remember, this is another way of writing a translation. So what this really means is that each point is not going to move left or right, but they will move up to, according to this translation, Mathematically, what it means is we&#x27;re going to keep the X value of each point. But I had to teach y value. So let&#x27;s get started. So our first vertex is a negative one. Negative one. So under the transformation, I&#x27;m going to keep negative, won the X value and add to to the y value. So the image of this point is negative one one. So our next point 01 under the transformation, we will keep the X value, and we will add to the y value. So I get an image of zero comma three and our last Vertex is that 40 So, under the transformation, I will keep the X, and I will add to to the y value. So our image is that for two. So these are the images of the use of urgencies of the strangle. Under this transformation

Erin Kirchmeier · Answer

in this problem, you&#x27;re given the vergis ease of a triangle in the coordinate plain and were asked to find the images of these points under this transformation. So if you recall, this is another way of writing a translation. So translation means the shape physically moves either up, down, left or right. So under this transformation, the point moves four to the right and one down. So that&#x27;s our translation. However mathematically, how we&#x27;re going to do this is we&#x27;re gonna take each point and we&#x27;re going to add four to the X value and take one away from the Y value. So let&#x27;s get started. Our first point is negative. One negative one. So negative one comma, negative one. We&#x27;re going to take negative won the X value, not forward to it. Then we&#x27;re going to take the Y value negative one and subtract one from it. So this gives us the 0.3 comma negative to as our image of this point, our next point is 01 So we&#x27;re gonna take that and we&#x27;re going to add for two R X value, and we&#x27;re going to subtract one from R A Y value. So this is going to give us the point for zero. And lastly, we ever last point for zero. We&#x27;re going to add for two R X value and we&#x27;re going to subtract one for Mara. Why about you? And this gives us the last point off a negative one. So here are the images of our original points under the given transformation.

Emily Min · Answer

So we have these four points G zero common zero h four come before I for common negative for and J a common zero. And we&#x27;re being asked to translate thes three units, the left and five units up. So how we&#x27;re gonna do this is we&#x27;re going to be using matrix addition. So first, let&#x27;s just craft this to see what we&#x27;re dealing with. So you have G zero common zero right here. The origin H for coming floor. You have I for common negative floor and we have J a common zero. So as you can see, this is like, sort of a square or a diamond, and it&#x27;s gonna be translated three and it&#x27;s to the left and five units up. So how we gonna set this up is we&#x27;re first gonna have a matrix for the original points, and we&#x27;re gonna set the top row is X and the bottom row as why this is gonna be G age. I n j. So four columns. So you have G is 00 h is for four. I is for negative for, and Jay is eight. Sirrah, that&#x27;s our first matrix. And we&#x27;re gonna be adding another matrix that represents this transformation over here. So if removing three units to the left, that means we&#x27;re gonna be moving wth e x coordinate to the left by three. So or subtracting three for each plane for the Y court in it. We&#x27;re moving five units up, so we&#x27;re gonna be adding five and then all we have to do here is on each and every point with the corresponding transmission. So this is gonna be zero minus three is negative. Three four minus three is one for minister is one eight. Ministers, five zero plus five is 54 plus fighters. Nine negative. Four plus five is one surplus. Food is five. And again, this represents the X and Y coordinates. And this is gonna be our new syriza points. So it&#x27;s chief run each prime. I plan on engines. So you have negative 35 109 1 couple one and five qualified. So now let&#x27;s graft these points on the same graph already done here to G Prime is negative. 35 each. Crime is one. Come on, nine I find is one. Come one and Jay Prime is gonna be five. Come on. Five So let&#x27;s craft this negative. 35 19 11 and five. As you can see, it&#x27;s the same shape. It&#x27;s just removed. The left and up. There shouldn&#x27;t be any sort of dilation or change in size. So yeah, that is how you complete this problem using matrix addition.

Ankit Gupta · Answer

According to the question we have given figure and you find out. Do or what it is there. What is is our minus two. Go March 2 four. Coma minus three and minus four. Comma minus four in discussion. Foster ful. We right? These? What is? You know, matters mattered. Minus 24 minus four. Do minus three. Minus four in discussion. Says that there is work disease off triangle Daddy&#x27;s work diseases off triangle. We know that. And discussion says transformed by right. Three upto right. Three upto means the ad with three in a row and air David to, you know, second rope, dear is the value comes new metrics is 17 minus 14 minus one minus two. This is a new metrics. We said that there is our workplaces off the image What it sees off the image. And, uh, the caution says first off will be right. Vortices We have given in cushion Tu minus three, minus four. Caution save is left. Five up for left, five minutes. First throws a practice video five and up. Four means we add with four second rope. We have new metrics. Comes out is minus seven minus one minus nine 610 The coordinators off door. This is off. The final triangle is Daddy&#x27;s you delight in Oh, what is this form? There is one comma four savin coma minus one minus one comma minus two on the second. Components minus seven. Coma six minus one CO My one and minus nine. Coma zero.

Charles Carter · Answer

it&#x27;s us to reflect. Um ah, pre image over the line y equals x to do so. I just need about two point. But the Matrix 0110 It&#x27;s courtesy matrix. So the mercy matrix in this problem for X, Y and Z what? It&#x27;s gonna be one negative one. Why? Value&#x27;s going to negative for and my Z values. Give me seven. Negative one. I don&#x27;t know if I find the nuke or nets for Ex Prime. Why Prime and Ze prime ready? It&#x27;s just gonna be, uh, basically what this does. It just flips the Yanks and my so the negative one line negative for two and negative 17 And lastly, it wants us to graft the image in pre image to our why values range from negative forward a positive seven. Uh, someone give myself a little bit more room on the positive sign. Okay. My ex values range from negative for deposit of seven something. Give myself a little bit more room on the positive side. Okay. My pre image will be in red. So one negative one ex volumes have to negative for have seven negative one. The axe. Why? See? Okay, And then my image will be at the point. Negative 11 since this is all in the original is on the fourth quadrant. Did the image should all be in the second quadrant? Or why, you bet negative for two. Where&#x27;s the value? Will be a negative 17 And there&#x27;s our excellent plan. My prime in ze prime. Thank you, very.

Problem

In Exercises $3-8,$ find the $3 \times 3$ matrice…

Problem 2 Easy Difficulty

Use matrix multiplication to find the image of the triangle with data matrix $D=\left[\begin{array}{ccc}{5} & {2} & {4} \\ {0} & {2} & {3}\end{array}\right]$ under the transformation that reflects points through the $y$ -axis. Sketch both the original triangle and its image.

Answer

$\begin{aligned} R D &=\left[\begin{array}{cc}{-1} & {0} \\ {0} & {1}\end{array}\right]\left[\begin{array}{ccc}{5} & {2} & {4} \\ {0} & {2} & {3}\end{array}\right] \\ &=\left[\begin{array}{ccc}{-5} & {-2} & {-4} \\ {0} & {2} & {3}\end{array}\right] \end{aligned}$

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

Linear Algebra and Its Applications

Anna Marie V.

Kayleah T.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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$\begin{aligned} R D &=\left[\begin{array}{cc}{-1} & {0} \\ {0} & {1}\end{array}\right]\left[\begin{array}{ccc}{5} & {2} & {4} \\ {0} & {2} & {3}\end{array}\right] \\ &=\left[\begin{array}{ccc}{-5} & {-2} & {-4} \\ {0} & {2} & {3}\end{array}\right] \end{aligned}$

Linear Algebra and Its Applications

Anna Marie V.

Kayleah T.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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

Anna Marie V.

Kayleah T.

Caleb E.

Maria G.

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

Linear Algebra and Its Applications