Matrix teaser any suggestions?

In summary, to find two 2x2 matrices B and C such that AB = AC but B does not equal C, one can use variables for the elements of the B matrix and row reduce A to determine the necessary transformation. Alternatively, one can use the null space of A to find suitable components for B and C.
  • #1
LaraCroft
14
0
Let A =

[ -3 9 ]
[ -1 3 ]

Find two 2x2 matrices B and C, such that AB = AC BUT B does not equal C.

I am stumped, but I am trying inverses and such, with no luck :(

Any insight would be great!:wink:
 
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  • #2
LaraCroft said:
Let A =

[ -3 9 ]
[ -1 3 ]

Find two 2x2 matrices B and C, such that AB = AC BUT B does not equal C.

I am stumped, but I am trying inverses and such, with no luck :(

Any insight would be great!:wink:

Matrix A has rank 1. Any component of the column vectors in B and C in the null space of A will be mapped to zero. This leaves quite a few possibilities.

However, if you haven't learned about null spaces yet, Just use variables for the ellements of the B matrix, multiply A by B and see how these variables can be changed without affecting the product.

This might be more clear if you row reduce A. Remember that each row operation can be represented by a linear transformation. Doing the row operation on the identity matrix will give you the desired transformation. Therefor you can safely row reduce A without affecting the solution to the problem.
 

1. What is the Matrix teaser?

The Matrix teaser is a short promotional video released before the premiere of the film The Matrix. It provides a glimpse into the world and characters of the film, building anticipation for its release.

2. When was the Matrix teaser released?

The Matrix teaser was first released on September 7, 1998, nearly a year before the film's premiere date of March 31, 1999.

3. Who directed the Matrix teaser?

The Matrix teaser was directed by the Wachowski siblings, Lana and Lilly, who also wrote and directed the film.

4. What can we expect to see in the Matrix teaser?

The Matrix teaser gives a brief introduction to the film's main characters, including Neo, Trinity, and Morpheus. It also showcases the film's groundbreaking special effects and action scenes. Overall, the teaser sets the stage for the mind-bending and action-packed journey that the film will take viewers on.

5. Are there any easter eggs or clues hidden in the Matrix teaser?

Yes, there are several easter eggs and hidden clues in the Matrix teaser that foreshadow events and themes in the film. These include hidden binary code, references to Alice in Wonderland, and a glimpse of the red pill that plays a crucial role in the film's plot.

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