Solving a Matrix Problem: Help Appreciated!

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In summary, the conversation is about finding the values of a given matrix using a given polynomial function. The method of plugging in the diagonal values of the matrix into the polynomial function is shown, but it is mentioned that this method may not work for higher degree polynomials. The concept of a matrix minus a scalar multiple of the identity matrix is also discussed. The notation of using capitals for matrices and finding p(A) instead of p(a) is mentioned. The conversation concludes with the speaker thanking the expert for their help.
  • #1
JasonRox
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I'm studying for a test and I got stuck here.

Let A be the matrix:

3..1
2..1

In each part find p(a).

a) p(x)=x-2

The answer is:

1..1
2..-1

The only way I can see this happen is that we take the numbers on the diagonal and pluck it in p(x).

So...
x-2=3-2=1

x-2=1-2=-1

Leaving the others alone, we get.

1..1
2..-1


The problem is, I know this is WRONG. This method does not work for b) and c), which are polynomials of higher degrees.

The inverse is:

1..-1
-2..3

I still can see a solution pattern.

I tried to relate to the chapter, but no luck.

Any help is appreciated.
 
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  • #2
A matrix minus a scalar? That doesn't make any sense.
 
  • #3
It is a matrix minus a scalar multiple of the identity matrix.
 
  • #4
Let's say I choose 2x-2.

Would that be...

4..1
2..0

If this is correct, would x^2 imply multiplying both matrixes.
 
  • #5
first of all do follow the standard notations ...
we usually use capitals for matrices ...
secondly
2X - 2
more often than not implies
2X-2I
where I is the identity matrix ...
so u can see why the answer is the way it is ...

and yes X^2 implies multiplication of matrices ... i.e X*X

-- AI
 
  • #6
That's not what it says.

The question doesn't have capitals and refers to the matrix as A.
 
  • #7
jason,
it also asks u to find p(a)
now this is really bad use of the notation actually.

p(x) =x-2 is fine
but i would expect them say
find p(A) and not p(a)

and yes when u sub in a matrix for x in an equation (in x) .. the constant (say c) is dealt as c*I ..

-- AI
 
  • #8
I really appreciate your help.

I understand where you are coming from. This might be the reason why I didn't know what was going on.
 

1. What is a matrix problem?

A matrix problem is a mathematical problem that involves manipulating and solving equations using matrices, which are arrays of numbers or symbols arranged in rows and columns.

2. How do you solve a matrix problem?

To solve a matrix problem, you can use various methods such as Gaussian elimination, inverse matrices, and Cramer's rule. These methods involve using operations such as addition, subtraction, multiplication, and division to manipulate the equations and find the solution.

3. What are some common applications of matrix problems?

Matrix problems have many applications in fields such as engineering, physics, economics, and computer science. Some examples include solving systems of linear equations, analyzing data, and creating transformations in 3D graphics.

4. What are some tips for solving matrix problems more efficiently?

Some tips for solving matrix problems more efficiently include organizing the equations in a matrix format, using a calculator or computer software to perform calculations, and practicing with various methods to determine which one is most effective for a specific problem.

5. How can I get help with solving a matrix problem?

If you need help with solving a matrix problem, you can consult a teacher, tutor, or online resources such as tutorials, practice problems, and forums. It can also be helpful to work through problems with a study group or seek guidance from more experienced individuals.

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