High School Mathematics Extensions/Matrices/Problem Set
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Problem Set[edit]
1. Zhuo decided to write a message to Jenny using matrix encryption. He substituted each letter in the English alphabet with a number:
- A to 0
- B to 1
- C to 2
- ...
- Z to 25,
he then wrote his message in a 2 by 4 matrix as follows
- ,
now he pre-multiplies his secret message X with a matrix to get the result
- .
What was Zhuo's message to Jenny?
2. A 2 by 2 matrix A has the following property
and .
What is the inverse of A?
3. Let
- ,
and let K = I + J. Show that K^{n} = nK.
4. Suppose
and
prove or disprove that you can always find a positive integer m such that
5. Let p and q be two real numbers such that p + q = 1. Show that there is a 2 × 2 matrix, A ≠ I (i.e. not equal to the identity) such that
6. Find A such that:
...more to come. Please contribute good problems