InterviewSolution
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InterviewSolution
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If\( \begin{bmatrix}x &x-y \\[0.3em]2x+y & 7\\[0.3em]\end{bmatrix}\)= \( \begin{bmatrix}3 &1 \\[0.3em]8 & 7\\[0.3em]\end{bmatrix}\), then find the value of y. |
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Answer» We are given that, \( \begin{bmatrix}x &x-y \\[0.3em]2x+y & 7\\[0.3em]\end{bmatrix}\)= \( \begin{bmatrix}3 &1 \\[0.3em]8 & 7\\[0.3em]\end{bmatrix}\) We need to find the value of y. We know by the property of matrices, \(\begin{bmatrix} a_{11}& a_{12} \\[0.3em] a_{21} & a_{22} \\[0.3em] \end{bmatrix}\)= \(\begin{bmatrix} b_{11}& b_{12} \\[0.3em] b_{21} & b_{22} \\[0.3em] \end{bmatrix}\) This implies, a11 = b11, a12 = b12, a21 = b21 and a22 = b22 So, if we have \( \begin{bmatrix}x &x-y \\[0.3em]2x+y & 7\\[0.3em]\end{bmatrix}\)= \( \begin{bmatrix}3 &1 \\[0.3em]8 & 7\\[0.3em]\end{bmatrix}\) Corresponding elements of two elements are equal. That is, x = 3 …(i) x – y = 1 …(ii) 2x + y = 8 …(iii) 7 = 7 To solve for y, We have equations (i), (ii) and (iii). From equation (i), x = 3 Substituting the value of x = 3 in equation (ii), x – y = 1 ⇒ 3 – y = 1 ⇒ y = 3 – 1 ⇒ y = 2 Thus, We get y = 2. |
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