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In-s [12.5K]
3 years ago
13

If A,B are n×n matrices, then (A + B)^2 = A^2 + 2AB + B^2. Either prove that this statement is true, or explain why it is false.

Mathematics
1 answer:
bonufazy [111]3 years ago
6 0
<h2>Answer:</h2>
  • The given statement is false.
  • The statement is necessarily true  when two matrix A and B commute.
<h2>Step-by-step explanation:</h2>

This statement is false.

Since, for two matrices A and B , the expansion of the term:

(A+B)^2 is given by:

(A+B)^2=(A+B)(A+B)\\\\i.e.\\\\(A+B)^2=A^2+B\cdot A+A\cdot B+B^2

Also, we know that when two matrix A and B commute then we have:

A\cdot B=B\cdot A

Hence, we get the expression as:

(A+B)^2=A^2+2A\cdot B+B^2

But when two matrix A and B do not commute then we need not have:

  (A+B)^2=A^2+2A\cdot B+B^2

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kakasveta [241]

The number of years value isn't given, we could use an hypothetical value, which can be substituted for the correct number of years given in your exercise in other to find the exact answer.

Using a t value of 10 years

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651558

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Given that:

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Using the relation :

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Answer:

1. 3/6 or 3 out of 6

2. 6 times

3. 50.24mm²

4. 2.4

5. -4/3

6. 6 i think, but i'm not positive on this one

have a wonderful day :)

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