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In: Advanced Math

Consider a square matrix A such that Ker(A2 ) = Ker(A3 ). Is Ker(A3 ) =...

Consider a square matrix A such that Ker(A2 ) = Ker(A3 ). Is Ker(A3 ) = Ker(A4 ). Explain your reasoning.

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Expert Solution

Let A be a square matrix such that .

Let .

Then,

    [matrix multiplication isassociative]

.

Then,

So,

Now, let .

Then,

    [matrix multiplication isassociative]

.

Since and , then

    [matrix multiplication isassociative]

.

Then,

So,

So, from (1) and (2), .

Colby Messinger answered 2 years ago
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