For A = 1, 2; 3, 4 there are numbers p and q such that A² = pA + qI. Find p and q.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
For $A =
pqA² = pA + qIpq$.
Need a reminder? The key ideaShow
is row of multiplied by column of , and exists when the columns of equal the rows of . Matrix multiplication is associative and distributive but not commutative. The entry of counts routes with steps.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The square. $A² =
$.
Step 2. The right side. $pA + qI =
$.
Step 3. Match entries. gives . Then gives .
Check. and , as required.
Answer: and , so .
Discussion (0)
Log in to join the discussion.
Loading…