High School Mathematics Extensions/Matrices/Problem Set

From Wikibooks, open books for an open world
Jump to navigation Jump to search
HSME
Content
100% developed Matrices
100% developed Recurrence Relations
Problems & Projects
100% developed Problem Set
100% developed Project
Soultions
100% developed Exercises Solutions
50% developed Problem Set Solutions
Misc.
100% developed Definition Sheet
100% developed Full Version

Problem Set[edit | edit source]

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

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


6. Find A such that:

...more to come. Please contribute good problems