Question

This is very, very urgent!!
It is matrices question
Find the real numbers a and b if
aX^2 + bX = 2*I
and
X =
[2 1]
[1 3]

I found out what is X^2 but I don't get what 2*I means and how to then get values for a and b

Much appreciation in advance!

Answer 1

2*I is just 2 times the identity matrix. So \[2I=\left[\begin{matrix}2&0\\0&2\end{matrix}\right]\]

Answer 2

So you have X and X^2. Now you just need to find an a, b such that when you add aX^2+bX you get the matrix just typed out.

Answer 3

Is identity matrix the one where you zero (times 0) all values in the original matrix except those that draw diagonal from upper left to lower right? if so i dont get how'd you get 2 0 (upper row) and 0 2 (lower row) instead of 0 3 lower row? Or then the identity matrix means something else..? :S

Answer 4

just think you are multiplying 2 by every value in the identity matrix

Answer 5

The identity matrix is \[I=\left[\begin{matrix}1&0\\0&1\end{matrix}\right]\] but when you multiply by 2, you just multiply each entry by 2. So\[2I=\left[\begin{matrix}2\cdot1&2\cdot0\\2\cdot0&2\cdot1\end{matrix}\right]=\left[\begin{matrix}2&0\\0&2\end{matrix}\right]\]

Answer 6

Aah now I got it. Thanks mate!

Answer 7

You're welcome.

Let me know what you get for a, b if you want me to check your answer.

Answer 8

I got the answer : ) checked from book, thanks for the offer tho : p