MHB Some help on a matrix question please.

[khehrap]

View attachment 2019
Hi. I am wondering if I can get some help on one or two questions on the sheet attached. I have worked out A^2B but am a bit puzzled on the meaning of A^TB. It is probably something very simple but I am struggling could someone help me possibly by listing out steps?.

Also I have worked out A^-1 but am stuck on solving the system of equations. As I though that you have to work out the inverse of a matrix when doing it for equations (AX=B format). although when I work out A ((2,-1)(3,2)(5,3) it is a 3x2 matrix therefore I am unable to get an inverse. Although the numbers are the same as the A^-1 question but just missing 0's therefore I think it may be something to do with that. Could someone help me please.

Thanks
Prab

 

[khehrap]

Hi I think I may have solved the equations (entering 0s where p1 p2 or p3 do not exist in the equation)

Could someone please still help to see if I have done it correct.

 

[Evgeny.Makarov]

I have worked out A^2B but am a bit puzzled on the meaning of A^TB.

$A^T$ denotes the transpose of $A$.

Hi I think I may have solved the equations (entering 0s where p1 p2 or p3 do not exist in the equation)

Yes, in problem 2, the matrix of the system of equations is $A$.

Could someone please still help to see if I have done it correct.

Please post your results so that we can check.

 

[khehrap]

$A^T$ denotes the transpose of $A$.

Yes, in problem 2, the matrix of the system of equations is $A$.

Please post your results so that we can check.

Hi Evgeny
I ralised that filling in the 0's gives me a matrix that I can use. Although I had already worked out the A^-1 in the first part of the question. therefore working row by row as normal.
The only problem I am facing (must be a calculation error - been doing this assignment for a while is that when I try to work out p2 using matrix inversion shown below:

[1.250 x 2] + [0.375 x 16] + [-0.500 x 21] I am getting -4 not +4. Whereas the answer is +4 (calculation works correctly for both p1 and p3 giving me 3 and 2 respectively.)

I am using the figures above as a-1 gives the figures stated.

I have answered the cramers part too and been given the results 3 4 and 2 for p1 p2 p3.

Thanks

 

[Evgeny.Makarov]

[1.250 x 2] + [0.375 x 16] + [-0.500 x 21] I am getting -4 not +4.

The middle number in $A^{-1}$ is $6/8=0.75$, not 0.375. See WolframAlpha.