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9514 1404 393
Answer:
6. see attached
7. (a, b) = (-2, 3)
8. equation has issues
Step-by-step explanation:
6. Matrix addition is defined for corresponding terms, so the usual associative and commutative properties of addition apply. That is, ...
A₁₁ +B₁₁ = (A+B)₁₁ . . . . . and the same for other corresponding terms
The attachment shows the sums are equal. (It is convenient to let a spreadsheet do the tedious repetitive work.)
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7. To find 'a' and 'b', we only need to consider the matrix elements that involve those variables.
element 11: 5 = b +2 ⇒ b = 3
element 21: a = 2 +2a ⇒ a = -2 (add -a-2 to both sides to get this)
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8. There are issues with this equation. It is incomplete and inconsistent.
element 11: p = p+4 ⇒ no solution
element 21: r = 0 +(2r s) ⇔ missing math symbol; problem is incomplete
element 12: q = 6 + (p +q) ⇒ p = -6; q = anything
element 22: s = 2s +2 ⇒ s = -2 (add -s-2 to both sides)
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<em>Additional comment</em>
When a problem has issues of the kind that show up in question 8, I suggest that you have your teacher show you how to work the problem. If they're paying attention, they will discover the issues for themselves.
If they are able to work the problem, it will be because they filled in the missing information and resolved the inconsistencies. This will let you see the intended question.
You can use the definition of prime polynomials to find out which polynomial is prime and which is not.
The prime polynomials in the given options are:
Option 1:
Option 3:
Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.
(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)
<h3>Which of the given polynomials are prime?</h3>Option 1:
We have to check it manually. The roots of this equation are
not integer or integer fraction (checked from calculator), and does't factor into smaller integer coefficient polynomials.
(you can check if its getting factored, manually, and most of the times, if it is not prime, it will get factored).
Thus, it is a prime polynomial.
Option 2:
We can rewrite it as
Thus, it is possible to write it as product of lower degree polynomial with integer coefficients, thus it is not a prime polynomial.
Option 3:
Since 3 is prime number and since given polynomial is quadratic thus lower degree would be only linear, thus, let
b is not a real number, so the factorization is not polynomial factorization.
Thus, it is prime polynomial.
Option 4:
We can rewrite it as:
Thus, not a prime polynomial.
Option 5:
We can rewrite it as:
Thus, not a prime polynomial.
Thus,
The prime polynomials in the given options are:
Option 1:
Option 3:
Learn more about prime polynomials here: