Check/verify my work and answer? Pseudoinverse of matrix

[Math100]

Homework Statement

I will upload my work and answer for this math problem. Can someone please check/verify if my work and answer is correct/incorrect?

Relevant Equations

None.

Also, if it's possible, I would really like to know the command for inputting this kind/type of problem on Ti-89 in order to check correct answers for linear algebra problems like this one.

 

[docnet]

You should calculate the inverse matrix using
$\begin{bmatrix} a & b \\ c & d \end{bmatrix}^{-1} = \frac{1}{ac-bd}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$
edit: you can also check your answer by matrix multiplication

 

[suremarc]

Instead of having to ask us, here is a simple way to check: multiply the resulting matrix by $A$.

Also, I think it is worth mentioning that OP appears to have written $\begin{bmatrix}\frac{1}{3} & -\frac{1}{3} \\ -\frac{1}{3} & \frac{5}{6}\end{bmatrix}$. I confused the /‘s with 1’s.

P.S., please use LaTeX instead of uploading your handwriting. The LaTeX guide can be found here.

 

[mfb]

I changed the title to make it more descriptive. The old title didn't have the topic of the question.

Instead of having to ask us, here is a simple way to check: multiply the resulting matrix by $A$.

That's the nice feature of calculating (pseudo)inverse matrices, they come with a simple cross-check.

1 and the division symbol look identical to me which is quite confusing.

 

[Mark44]

1 and the division symbol look identical to me which is quite confusing.

Very much so.
The $(A^TA)^{-1}$ matrix looked like $\begin{bmatrix} 113 & -113 \\ -113 & 516\end{bmatrix}$ at first glance, and similar problems in most of the others.
@Math100, to make your work more readable, make the / symbol look different from 1.

 

[Math100]

Very much so.
The $(A^TA)^{-1}$ matrix looked like $\begin{bmatrix} 113 & -113 \\ -113 & 516\end{bmatrix}$ at first glance, and similar problems in most of the others.
@Math100, to make your work more readable, make the / symbol look different from 1.

Yes, I'm so sorry about the confusion. It's meant to be fractions.