Find the value of x and y such that \(\left[ {\begin{array}{*{20}{c}} {x - y}\\ {x + y} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 2\\ 16 \end{array}} \right]\)

  1. x = 7 and y = 9
  2. x = 9 and y = 7
  3. x = 8 and y = 5
  4. x = 13 and y = 3

Answer (Detailed Solution Below)

Option 2 : x = 9 and y = 7
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Detailed Solution

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Concept:

If A and B are two matrices then A = B ⇔ A and B are of same order and the corresponding elements of A and B are same.

Calculation:

Given: \(\left[ {\begin{array}{*{20}{c}} {x - y}\\ {x + y} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 2\\ 16 \end{array}} \right]\)

As we know that, if A and B are two matrices then A = B ⇔ A and B are of same order and the corresponding elements of A and B are same.

⇒ x - y = 2--------(1)

⇒ x + y = 16---------(2)

On adding equation (1) and (2) we get,

⇒ x = 9

Now by substituting x = 6 in equation (1) we get

⇒ 9 + y = 16 ⇒ y = 7

Hence, x = 9 and y = 7

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