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Author: nsharp1
No. Questions: 4
Created: Oct 3, 2019
Last Modified: 5 years ago

Determinant of Transformation Matrices

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For the following questions, let T=[2-203] be a transformation matrix. Also, let V1=[255222-1-1] be the vertex matrix of a square whose area is 9 units squared.
Grade 12 Matrices CCSS: HSN-VM.C.12
A.
What is the resulting matrix if V1 is transformed by T? Let this matrix be V2.
  1. [0612666-3-3]
  2. [065266-1-1]
  3. [2682063-1]
  4. [41010466-3-3]
Grade 12 Matrices CCSS: HSN-VM.C.12
B.
What is the area of the resulting shape, defined by the vertex matrix V2?
  1. 108 units squared
  2. 72 units squared
  3. 54 units squared
  4. 36 units squared
Grade 12 Matrices CCSS: HSN-VM.C.12
D.
How does the absolute value of the determinant of the transformation matrix relate to the area of the two quadrilaterals (the square, S1 and the transformed shape, S2)? Choose the equation which correctly describes this relationship.
  1. |det(T)|=Area(S1) Area(S2)
  2. Area(S2)=|det(T)| Area(S1)
  3. |det(T)|=|Area(S2)-Area(S1)|
  4. There is no relationship between the absolute value of the determinant of T and the area of the shapes.