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Mathematics

If matrix A = [x−yx+yy−xy+x]\begin{bmatrix}[r] x - y & x + y \ y - x & y + x \end{bmatrix} and matrix B = [x+yy−xx−yy+x]\begin{bmatrix}[r] x + y & y - x \ x - y & y + x \end{bmatrix}, then A + B is :

  1. [2y2x02(x+y)]\begin{bmatrix}[r] 2y & 2x \ 0 & 2(x + y) \end{bmatrix}

  2. [2x2(x+y)00]\begin{bmatrix}[r] 2x & 2(x + y) \ 0 & 0 \end{bmatrix}

  3. [2x2y02(x+y)]\begin{bmatrix}[r] 2x & 2y \ 0 & 2(x + y) \end{bmatrix}

  4. [2x−2y2y00]\begin{bmatrix}[r] 2x - 2y & 2y \ 0 & 0 \end{bmatrix}

Matrices

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Answer

Substituting values of A and B in A + B, we get :

⇒A+B=[x−yx+yy−xy+x]+[x+yy−xx−yy+x]=[x−y+x+yx+y+y−xy−x+x−yy+x+y+x]=[2x2y02(x+y)].\Rightarrow A + B = \begin{bmatrix}[r] x - y & x + y \ y - x & y + x \end{bmatrix} + \begin{bmatrix}[r] x + y & y - x \ x - y & y + x \end{bmatrix} \\[1em] = \begin{bmatrix}[r] x - y + x + y & x + y + y - x \ y - x + x - y & y + x + y + x \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 2x & 2y \ 0 & 2(x + y) \end{bmatrix}.

Hence, Option 3 is the correct option.

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