InterviewSolution
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InterviewSolution
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Find the value of y if \(\begin{bmatrix} x-y& 2 \\[0.3em] x &5\\[0.3em] \end{bmatrix}\)= \(\begin{bmatrix} 2& 2\\[0.3em] 3 & 5 \\[0.3em] \end{bmatrix}\). |
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Answer» We are given that, \(\begin{bmatrix} x-y& 2 \\[0.3em] x &5\\[0.3em] \end{bmatrix}\)= \(\begin{bmatrix} 2& 2\\[0.3em] 3 & 5 \\[0.3em] \end{bmatrix}\) We need to find the values of x and 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 \(\begin{bmatrix} x-y& 2 \\[0.3em] x &5\\[0.3em] \end{bmatrix}\)= \(\begin{bmatrix} 2& 2\\[0.3em] 3 & 5 \\[0.3em] \end{bmatrix}\) Corresponding elements of two matrices are equal. That is, x – y = 2 …(i) 2 = 2 x = 3 …(ii) 5 = 5 To solve for x and y, We have equations (i) and (ii). From equation (ii), x = 3 Substituting x = 3 in equation (i), we get 3 – y = 2 ⇒ y = 3 – 2 ⇒ y = 1 Thus, We get x = 3 and y = 1. |
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