MI 4 Vectors Supplement to 7
Name ___________________________
 3 2
1. Let A  
 1 2
a. Find A  B
 12
12 
 and B  
3 2 
  3 2
3 2

1 2 
b. Find B  A
c. Identify the transformation represented by each of the above matrices, A, B, and A  B .
2. Find a single matrix that Rotates 30° clockwise and reflects over the line y  x .
3. Does order matter in how you do problem 2? Explain.
4. Find a single matrix that does the following in the given order:
1) Changes the scale (dilation): x  2x , y  3 y
2) Rotates 45° clockwise.
3) Reflects over the y-axis.
MI 4 Vectors Supplement to 7
5. Apply your transformation matrix to the triangle A: (0, 1), B: (2, 3), C: (-2, 2). Graph the
original triangle, then the result of doing each transformation above in order (you will have 4
triangles graphed). Finally, multiply your matrix from problem #4 times the triangle matrix
and see if you have the same result.
6. Find the matrix that undoes the above, (i.e., transforms the image to the original triangle)
in two different ways, one with matrix multiplication and the other with inverse matrices.
MI 4 Vectors Supplement to 7
MI 4 Vectors Supplement to 7
Selected Answers
1)
 0 1
a) 

 1 0
 0 1
b) 

 1 0
c) A: Rotates 30° clockwise
B: Rotates 60° clockwise
A  B  B  A  Rotates 90° clockwise
3)
5)
Yes. One reflects and then rotates, the other rotates and then reflects. The operations are
not commutative.
 3 2

 2
3 2

 2
13 2
2
5 2
2

 2
 2.12 9.19 1.41
 or 


 2.12 3.54 7.07 
5 2
