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Find the solution for a 2x2 matrix A:

[4 4
0 1] to the nth power = [ ]

User Edwin Liu
by
8.4k points

2 Answers

3 votes

Answer:

A^n = [4^n 4^n

0 1]

Explanation:

To find the solution for the 2x2 matrix A:

[4 4

0 1] to the nth power = [ ]

We can use matrix multiplication to raise A to the nth power. Let's start with n = 1:

A^1 = [4 4

0 1]

Now, let's solve for A^2 by multiplying A^1 by A:

A^2 = A x A^1

= [4 4 [4 4

0 1] 0 1]

= [16 16

0 1]

Next, let's solve for A^3:

A^3 = A x A^2

= [4 4 [16 16

0 1] 0 1]

= [64 64

0 1]

We can see a pattern emerging:

A^1 = [4 4

0 1]

A^2 = [16 16

0 1]

A^3 = [64 64

0 1]

We can generalize this pattern as follows:

A^n = [4^n 4^n

0 1]

Therefore, the solution for the 2x2 matrix A raised to the nth power is:

A^n = [4^n 4^n

0 1]

User Rubens Mariuzzo
by
8.9k points
5 votes

Answer:

Explanation:

User Kimy
by
7.9k points

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