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3 years ago

If a,b, and c are prime numbers, do (a+b)(a+b) and cc have a common factor that is greater than 1?

Mathematics

1 answer:

Tanya [424]3 years ago

3 0

Answer:

1. Information is not sufficient

2. Information is not sufficient

Step-by-step explanation:

Question Modified

If a,b, and c are prime numbers, do (a+b) and c have a common factor that is greater than 1?

(1) a,b, and c are all different prime numbers

(2) c≠2

Explanation

1. Let's assume values of 1,3 and 5 to a, b, and c respectively

a + b = 1+3 = 4

4 and 5 do not have any common factor aside 1

Let's assume values of 1,3 and 2 to a,b and c respectively

a + b = 1+3 = 4

4 and 2 have a common factor of 2

So, the available information is not sufficient

Let's assume values of 2,7 and 3 to a b and c response

a + b = 2 + 7 = 9

9 and 3 have a common factor of 3

Also, let's assume values of 2,7 and 5 to a, b and c

a + b = 2 + 7 = 9

9 and 5 do not have a common factor

So, the available information is also not sufficient to answer the question.

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Step-by-step explanation:

Since we have given that

A and B are 4 × 4 matrices.

Here,

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We need to find the respective parts:

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b) det (B⁵ )

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c) det (2A)

Since we know that

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Since we know that

$\mid A^T\mid=\mid A\mid$

so, it becomes,

$\mid A^TA\mid=\mid A^T\mid \times \mid A\mid=-3\times -3=9$

e) det (B⁻¹AB)

As we know that

$\mid B^{-1}\mid =\mid B\mid$

so, it becomes,

$\mid B^{-1}AB}\mid =\mid B^{-1}.\mid \mid A\mid.\mid B\mid=2\times -3\times 2=-12$

Hence, a) -6, b) 32, c) -48, d) 9, e) -12

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Step-by-step explanation:

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