Alg1231W6T3 - Linear transformations through pictures

Sunday, 2 September 2018

6:29 PM

Untitled picture.png Machine generated alternative text: Figure 1. A colourful house -2 c A 2 Suppose OE 7 8 Under the transformation S(x) 3 2 Nx where N is (t) and = we find that S(OA) It follows that S(öö) = S(OE) - vectoræ, = 7/2, (2) = 9' 1 Recall: the Maple notation for the vector is < 1,2 2 Untitled picture.png Machine generated alternative text: Figure 1. The same colourful house -2 2 Suppose OE we find that T(OA) 7 8 3 2 Under the transformation T(x) Mx , where M is 2 -1 c A 4 2 and T(OB) -1 4 T(OC) — T(OD) — T(OE) — vectoræ, = 2, (2) = 3}) Vector(2, = 7/4, (2) = 1 Recall: the Maple notation for the vector 2 Untitled picture.png Machine generated alternative text: with(LtnearÅ lgebra) 03 Multiply(N, (1, 1)) 4 Multiply(N, 1.5)) Multiply N, 2. 450000000000000 2 9 2
Untitled picture.png Machine generated alternative text: Figure 1. The same colourful house -2 2 Suppose OE we find that T(OA) 7 8 3 2 Under the transformation T(x) Mx , where M is 2 -1 c A 4 2 and T(OB) -1 4 T(OC) — T(OD) — T(OE) — vectoræ, = 2, (2) = 3}) Vector(2, = 7/4, (2) = 1 Recall: the Maple notation for the vector 2 Untitled picture.png Again suppose that OE Under the transformation R(x) Figure 1 The same colourful house Lx , where L is we find that R( R(OC) R(OD) — R(OE) and R(OB) vector(2, = 5., (2) = 2.5 so Untitled picture.png Machine generated alternative text: with(LtnearÅ lgebra) Multiply(N, (1, 1)) 2 Multiply(N, 1.5)) Multiply N, 4 41 Untitled picture.png with(LtnearÅ lgebra) 13 -12 Multiply(N, (1, 1)) 4 Multiply(N, 1.5)) Multiply N, 250000000000000 43 17
Untitled picture.png Again suppose that OE Under the transformation R(x) Figure 1 The same colourful house Lx , where L is we find that R( R(OC) R(OD) — R(OE) and R(OB) vector(2, = 5., (2) = 2.5 so Untitled picture.png Which of the following is the image of the house under the transformation R? For convenience, these diagrams have been scaled dowm Untitled picture.png with(LtnearÅ lgebra) 13 -12 Multiply(N, (1, 1)) 4 Multiply(N, 1.5)) Multiply N, 250000000000000 43 17
Untitled picture.png Which of the following is the image of the house under the transformation R? For convenience, these diagrams have been scaled dowm Untitled picture.png Consider the matrix "renovation" U that will transform our house in figure 1 into the house in Figure 2 below Figure 1. The usual house, without the marked points Figure 2_ The transformed house Untitled picture.png 2 o +2 1 2 4 5 Playing with the app above (or otherwise), we see that the matrix representation for this linear transformation would be K This transformation would send v Recall: the Maple notation for the matrix 112 >,< 314
Untitled picture.png 2 o +2 1 2 4 5 Playing with the app above (or otherwise), we see that the matrix representation for this linear transformation would be K This transformation would send v Recall: the Maple notation for the matrix 112 >,< 314 Untitled picture.png Figure 1 _ A logo Figure 2 The transformed logo A designer wants to arrange a transformation R to take the image in Figure 1 to the image in Figure 2. Unfortunately she didn't take a first year maths course at UNSWI but we can help her by looking fora linear O transformation to do the job; i.e. something of the form ax + by The definition of the map R tells us that and R( Untitled picture.png with(LtnearÅ lgebra) Multiply(N, ( 1 , 4)) 21 02 -6
Untitled picture.png Figure 1 _ A logo Figure 2 The transformed logo A designer wants to arrange a transformation R to take the image in Figure 1 to the image in Figure 2. Unfortunately she didn't take a first year maths course at UNSWI but we can help her by looking fora linear O transformation to do the job; i.e. something of the form ax + by The definition of the map R tells us that and R( Untitled picture.png and the diagram tells us Note: the Maple notation for the vector Hence; after a little bit of algebra; we deduce that 1,2 > and satisfy the equation [select all that apply] 2 To check our result; we note that if x + y 5X2 - 2XY+2Y2 = 9 (X - + (2X+Y)2 5X2 +2XY+2Y2 = 1. 1 then
Untitled picture.png and the diagram tells us Note: the Maple notation for the vector Hence; after a little bit of algebra; we deduce that 1,2 > and satisfy the equation [select all that apply] 2 To check our result; we note that if x + y 5X2 - 2XY+2Y2 = 9 (X - + (2X+Y)2 5X2 +2XY+2Y2 = 1. 1 then

 

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