Finding Matrix B from given info

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In summary, the conversation discusses finding matrix B using the equation (I + 3B)^-1 = [5 2; 4 2]. The individual attempted to solve the equation by multiplying both sides by I + 3B and setting the product equal to the identity matrix, but was unsuccessful in finding the correct matrix B. The suggestion is made to simply calculate the matrix inverse of the 2x2 matrix on the right-hand side of the equation.
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xipe
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Homework Statement


Use the given info to find matrix B

Homework Equations


(I + 3B)^-1 = [5 2; 4 2]

to make more clear:

inv(I + 3B) = this 2x2 matrix: top row = 5 2, bottom row = 4 2

The Attempt at a Solution


I tried multiplying both sides of the eqn by I + 3B to get I = [5 2; 4 2](I + 3B)
Then tried to multiply the two quantities (using B = [a b; c d])
Tried to set that product equal to the identity matrix and solve for the unspecified constants, a b c d.
After that I plugged the values into the the product found in the previous step
I then should have acquired the correct matrix B, but alas, it wasn't even close.
If I am overlooking some elementary matrix 'algebra', or any hints at all would be greatly appreciated.
Thank you!
 
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  • #2
Why not just calculate the matrix inverse of the 2x2 matrix on the RHS?
 

1. How do I find Matrix B from given information?

To find Matrix B, you will need to have the given information, which includes the dimensions of the matrix, the values of the elements, and the operations needed to manipulate the matrix. Once you have all this information, you can use different methods such as row operations or matrix multiplication to find Matrix B.

2. What is the importance of finding Matrix B?

Finding Matrix B is important because it allows you to solve systems of linear equations, perform transformations, and calculate determinants and inverses of matrices. It is also a fundamental step in further mathematical and scientific calculations.

3. Can I use any method to find Matrix B?

Yes, there are various methods to find Matrix B, such as using row operations, matrix multiplication, or using software programs like MATLAB or Excel. The method you choose will depend on the given information and the complexity of the matrix.

4. What is the difference between finding Matrix B and Matrix A?

Matrix B is typically used to represent the changed or transformed version of Matrix A. To find Matrix B, you will need to perform certain operations on Matrix A, such as adding, subtracting, or multiplying by a scalar value. Matrix A, on the other hand, represents the original values of the matrix before any transformations are applied.

5. Are there any shortcuts or tricks to finding Matrix B?

There are no shortcuts or tricks to finding Matrix B. It requires following a systematic approach and using mathematical operations to manipulate the given information. However, with practice and familiarity with matrix operations, you may be able to find more efficient ways to calculate Matrix B.

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