# Math Help - [SOLVED] some matrices help

1. ## [SOLVED] some matrices help

hi, some more matrices problems that i can't solve
no 1 :

a) Find PQ which i did =

i can't solve b which is

b) Find a matrix X such that PX + Q = P

no2) If work out $x^{2}$ and $X ^{3}$

hence show that $X^{3} = 4X - X^{2} + I$

i worked out x^2 and X^3 , and i tried doing the above calculations but didn't get x^3
what should i do?

2. For #1b you must first find $P^{-1}$.
Then $X=P^{-1}(P-Q)$.

#2 is just a matter of doing all the caculations correctly.

3. Originally Posted by llkkjj24
no2) If work out $x^{2}$ and $X ^{3}$

hence show that $X^{3} = 4X - X^{2} + I$

i worked out x^2 and X^3 , and i tried doing the above calculations but didn't get x^3
what should i do?

Hi llkkjj24,

$X=\left[\begin {array}{ccc}1 & 0 & 1 \\ 0 & -2 & 1 \\ 1 & 1 & 0 \end{array}\right] \: \: X^2=\left[\begin {array}{ccc}2 & 1 & 1 \\ 1 & 5 & -2 \\ 1 & -2 & 2 \end{array}\right]\: \: X^3=\left[\begin {array}{ccc}3 & -1 & 3 \\ -1 & -12 & 6 \\ 3 & 6 & -1 \end{array}\right]$

$X^3=4X-X^2+I$

$\left[\begin {array}{ccc}3 & -1 & 3 \\ -1 & -12 & 6 \\ 3 & 6 & -1 \end{array}\right]=4\left[\begin {array}{ccc}1 & 0 & 1 \\ 0 & -2 & 1 \\ 1 & 1 & 0 \end{array}\right]-\left[\begin {array}{ccc}2 & 1 & 1 \\ 1 & 5 & -2 \\ 1 & -2 & 2 \end{array}\right]+\left[\begin {array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]$

4. As Plato points out, you need to know the inverse of P to solve the first part. Did you notice what the value of PQ is? If so, what is Q?

5. thanks, i noticed for no1 i did a mistake, i multiplied x^2 with x^2 instead of multiplying it with X to get x^3

6. Originally Posted by qmech
As Plato points out, you need to know the inverse of P to solve the first part. Did you notice what the value of PQ is? If so, what is Q?
yes, Q is the inverse of P

7. thanks guys, problem solved