# Check/verify my work and answer? Pseudoinverse of matrix

• Math100
In summary, the conversation discusses a method for checking correct answers for linear algebra problems on Ti-89 using inverse matrices. The formula for calculating inverse matrices is provided and it is mentioned that the resulting matrix can be multiplied by the original matrix for a simple cross-check. The confusion caused by using fractions and division symbols is also addressed.
Math100
Homework Statement
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.

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• Pseudoinverse.jpg
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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}##

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.

docnet, SammyS and berkeman
I changed the title to make it more descriptive. The old title didn't have the topic of the question.
suremarc said:
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.

docnet
mfb said:
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.

docnet
Mark44 said:
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.

docnet

## 1. What is a pseudoinverse of a matrix?

A pseudoinverse of a matrix is a mathematical operation that is used to find a generalized inverse of a non-square matrix. It is also known as the Moore-Penrose inverse and is often used in solving systems of linear equations.

## 2. How do I calculate the pseudoinverse of a matrix?

The pseudoinverse of a matrix can be calculated using various methods, such as the Singular Value Decomposition (SVD) method or the Least Squares method. The specific method used will depend on the size and properties of the matrix. It is recommended to use a computer program or calculator to calculate the pseudoinverse.

## 3. Why is the pseudoinverse important?

The pseudoinverse is important because it allows us to find a solution to a system of linear equations even when the matrix is not invertible. It also has applications in data analysis, signal processing, and machine learning.

## 4. What is the difference between a pseudoinverse and a regular inverse?

A regular inverse of a matrix only exists for square matrices, while a pseudoinverse can be calculated for any type of matrix. Additionally, the pseudoinverse is not a true inverse as it does not always satisfy the properties of a regular inverse, but it serves a similar purpose in solving systems of linear equations.

## 5. Can the pseudoinverse of a matrix be used to solve any problem?

No, the pseudoinverse can only be used to solve systems of linear equations. It cannot be used for other types of problems, such as finding eigenvalues or eigenvectors.

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