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2. The smiley face shown at the top of the figure¹ is transformed by various linear transforma- tions represented by matrices A - F. (a) Find out which matrix does which transformation. Write the letter of the correct trans- formation matrix next to the transformed image. Hint: Take a specific feature such as the tongue and assign a possible approximate coordinate, maybe (1, -1) and see how that vector transformed by multiplication by each matrix. The Slider Demonstration from David's Austin's Understanding Linear Algebra can be helpful in determining the transformations. https://understandinglinear algebra.org/sec-transforms-geom.html A = D = 0 (19) - ( 3 ) = ( 7 ) 0 B= (01) E C= = ( -1/2 16²). F = ( }). 0 image A-F image A-F image (b) Answer the following questions. i. Find a single matrix that would perform the following transformation on the smi- ley face image You can assume that the image is centered at the origin: Reflect 1Oliver Knill, Harvard. 3 the image about the x-axis, followed by a rotation through 7/6 counterclockwise, followed by an enlargement (dilation) of the smiley face image by a factor of 5. ii. If tongue of the smiley face it at the point (4). find the image of this point under the sequence of transformations given above.

2. The smiley face shown at the top of the figure¹ is transformed by various linear transforma- tions represented by matrices A - F. (a) Find out which matrix does which transformation. Write the letter of the correct trans- formation matrix next to the transformed image. Hint: Take a specific feature such as the tongue and assign a possible approximate coordinate, maybe (1, -1) and see how that vector transformed by multiplication by each matrix. The Slider Demonstration from David's Austin's Understanding Linear Algebra can be helpful in determining the transformations. https://understandinglinear algebra.org/sec-transforms-geom.html A = D = 0 (19) - ( 3 ) = ( 7 ) 0 B= (01) E C= = ( -1/2 16²). F = ( }). 0 image A-F image A-F image (b) Answer the following questions. i. Find a single matrix that would perform the following transformation on the smi- ley face image You can assume that the image is centered at the origin: Reflect 1Oliver Knill, Harvard. 3 the image about the x-axis, followed by a rotation through 7/6 counterclockwise, followed by an enlargement (dilation) of the smiley face image by a factor of 5. ii. If tongue of the smiley face it at the point (4). find the image of this point under the sequence of transformations given above.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 6E
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2. The smiley face shown at the top of the figure¹ is transformed by various linear transforma- tions represented by matrices A - F. (a) Find out which matrix does which transformation. Write the letter of the correct trans- formation matrix next to the transformed image. Hint: Take a specific feature such as the tongue and assign a possible approximate coordinate, maybe (1, -1) and see how that vector transformed by multiplication by each matrix. The Slider Demonstration from David's Austin's Understanding Linear Algebra can be helpful in determining the transformations. https://understandinglinear algebra.org/sec-transforms-geom.html A = D = 0 (19) - ( 3 ) = ( 7 ) 0 B= (01) E C= = ( -1/2 16²). F = ( }). 0 image A-F image A-F image (b) Answer the following questions. i. Find a single matrix that would perform the following transformation on the smi- ley face image You can assume that the image is centered at the origin: Reflect 1Oliver Knill, Harvard. 3 the image about the x-axis, followed by a rotation through 7/6 counterclockwise, followed by an enlargement (dilation) of the smiley face image by a factor of 5. ii. If tongue of the smiley face it at the point (4). find the image of this point under the sequence of transformations given above.
Transcribed Image Text:2. The smiley face shown at the top of the figure¹ is transformed by various linear transforma- tions represented by matrices A - F. (a) Find out which matrix does which transformation. Write the letter of the correct trans- formation matrix next to the transformed image. Hint: Take a specific feature such as the tongue and assign a possible approximate coordinate, maybe (1, -1) and see how that vector transformed by multiplication by each matrix. The Slider Demonstration from David's Austin's Understanding Linear Algebra can be helpful in determining the transformations. https://understandinglinear algebra.org/sec-transforms-geom.html A = D = 0 (19) - ( 3 ) = ( 7 ) 0 B= (01) E C= = ( -1/2 16²). F = ( }). 0 image A-F image A-F image (b) Answer the following questions. i. Find a single matrix that would perform the following transformation on the smi- ley face image You can assume that the image is centered at the origin: Reflect 1Oliver Knill, Harvard. 3 the image about the x-axis, followed by a rotation through 7/6 counterclockwise, followed by an enlargement (dilation) of the smiley face image by a factor of 5. ii. If tongue of the smiley face it at the point (4). find the image of this point under the sequence of transformations given above.
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