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 Kn = nK.

4. Suppose


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, AI (i.e. not equal to the identity) such that

6. Find A such that:

...more to come. Please contribute good problems