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Sagot :
Step-by-step explanation:
This is a inverse. matrix because we have alternating
zeroes and the w symbol it looks similar to the matrix,
[ 1 0]
[ 0 1]
Except, we just replace 1 with q. So we also know that if we multiply a inverse like matrix by itself, a infinite number times, it going to stay the same.
However, since we have variables in place for 1, we would raise the matrix to an nth power.
Because remeber that a inverse matrix has 1, an that
[tex]1 {}^{n} = 1[/tex]
So since we have a variable, we just raised it to the nth number.
We know that Zeroes raised to any power is 0, so w raised to the
^20226397596 is infact, w^20226397596, so our matrix is just
[w^20026397596 0]
[ 0 w^20026397596]
The value for [tex]A^{20226397596}[/tex] is [tex]\left[\begin{array}{cc}\omega^{20226397596}&0\\0&\omega^{20226397596}\end{array}\right] [/tex].
Procedure - Determination of the power of a matrix
Let be [tex]A[/tex] a diagonal matrix. By linear algebra we know that the n-th power of diagonal matrix of the form [tex]\left[\begin{array}{cc}\omega&0\\0&\omega\end{array}\right] [/tex] is equal to:
[tex]A^{n} = \left[\begin{array}{cc}\omega^{n}&0\\0&\omega^{n}\end{array}\right] [/tex], [tex]\forall\, n \ge 1[/tex], [tex]n\in \mathbb{N}[/tex] [tex]\forall \,\omega \in \mathbb{R}[/tex] (1)
Hence, we have the following result for [tex]A^{20226397596}[/tex]:
[tex]A^{20226397596} = \left[\begin{array}{cc}\omega^{20226397596}&0\\0&\omega^{20226397596}\end{array}\right] [/tex]
The value for [tex]A^{20226397596}[/tex] is [tex]\left[\begin{array}{cc}\omega^{20226397596}&0\\0&\omega^{20226397596}\end{array}\right] [/tex]. [tex]\blacksquare[/tex]
To learn more on matrices, we kindly invite to check this verified question: https://brainly.com/question/4470545
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