Step by Step solution about How to resolve the algorithm Matrix-exponentiation operator step by step in the Julia programming language

The provided Julia code raises the 2x2 matrix [1 1 ; 1 0] to the power of 10. This operation is known as matrix exponentiation and is useful in various mathematical and computational applications.

Here's a detailed explanation of the code:

1. [1 1 ; 1 0]: This is a 2x2 matrix defined using the [ ] notation. The semicolon ; separates the rows of the matrix.

2. ^10: This is the exponentiation operator in Julia. It raises the matrix to the power of 10, performing the matrix exponentiation operation.

3. The result is a 2x2 matrix of type Array{Int64,2}. The elements of the matrix are displayed as integers of type Int64.

The resulting matrix is:

2x2 Array{Int64,2}:
89  55
55  34

This means that raising the input matrix [1 1 ; 1 0] to the power of 10 gives a new matrix with the elements 89, 55, 55, and 34.

Matrix exponentiation is used in various applications, such as solving differential equations, finding eigenvalues and eigenvectors, and simulating dynamical systems. The result of the matrix exponentiation operation depends on the input matrix and the exponent.

julia> [1 1 ; 1 0]^10
2x2 Array{Int64,2}:
 89  55
 55  34