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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Additional comment
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.
