Order of 2x2 Matrix [[2 3][3 5]]

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In summary, the conversation discusses finding the order of a 2x2 matrix using the definition of the least power needed to raise the matrix to in order to get the identity matrix. The speaker also mentions the need to find the order in time proportional to the square root of the order. They are unsure about an algorithm for solving this problem in general and question the possibility of a solution for the given matrix.
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morningloree
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Hi!

I'm trying to find the order of a 2x2 matrix [[2 3][3 5]] (where the first row, from left to right, is 2 3 and the second row is 3 5). The definition of order that I am using is the least such power that I need to raise this matrix to in order to get the identity matrix. Also, I have to find the order in time proportional to the square root of the order, so I can't just do a linear search. Any help would be much appreciated!
 
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  • #2
I'm not sure about an algorithm for solving this problem in general - but unless I misunderstood the problem then you're solving:

[tex]A^k = I[/tex]

for A = [2,3;3,5] and k some integer? I'm pretty sure that a solution doesn't exist, as the values of the matrix will grow without bound as k goes large.
 

FAQ: Order of 2x2 Matrix [[2 3][3 5]]

What is a 2x2 matrix?

A 2x2 matrix is a rectangular array of numbers arranged in two rows and two columns. It is commonly used in mathematics, physics, and engineering to represent data and perform calculations.

What is the order of a matrix?

The order of a matrix refers to the number of rows and columns it has. For example, a 2x2 matrix has an order of 2 since it has 2 rows and 2 columns.

How do I multiply a 2x2 matrix by a scalar?

To multiply a 2x2 matrix by a scalar (a single number), you simply need to multiply each element in the matrix by that number. For example, if the matrix is [[2 3][3 5]] and the scalar is 2, the resulting matrix would be [[4 6][6 10]].

How do I add or subtract two 2x2 matrices?

To add or subtract two 2x2 matrices, you must ensure that they have the same order. Then, you simply add or subtract the corresponding elements in each matrix to get the resulting matrix. For example, if the matrices are [[2 3][3 5]] and [[1 2][2 3]], the resulting matrix would be [[3 5][5 8]].

How do I multiply two 2x2 matrices?

To multiply two 2x2 matrices, you must ensure that the number of columns in the first matrix is equal to the number of rows in the second matrix. Then, you multiply each element in the first row of the first matrix by each element in the first column of the second matrix, and add the products. This becomes the first element in the resulting matrix. Repeat this process for the remaining elements in the resulting matrix. For example, if the matrices are [[2 3][3 5]] and [[1 2][2 3]], the resulting matrix would be [[8 13][13 21]].

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