question_answer

Find the values of a and b, if A = B, where \[A=\left[ \begin{matrix}    a+4 & 3b  \\    8 & -\,6  \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix}    2a+2 & {{b}^{2}}+2  \\    8 & {{b}^{2}}-5b  \\ \end{matrix} \right].\]

Answer:

We have,           A = B             \[\Rightarrow \] \[\left[ \begin{matrix}    a+4 & 3b  \\    8 & -\,6  \\ \end{matrix} \right]=\left[ \begin{matrix}    2a+2 & {{b}^{2}}+2  \\    8 & {{b}^{2}}-5b  \\ \end{matrix} \right]\] On equating the corresponding elements, we get             \[a+4=2a+2\]                           ? (i)             \[3b={{b}^{2}}+2\]                            ? (ii) and       \[-\,6={{b}^{2}}-5b\]                           ? (iii) From Eq. (i), we get a = 2                     and from Eqs. (ii) and (iii), we get \[3b=(5b-6)+2\] \[\Rightarrow \] \[-\,2b=-\,4\] \[\Rightarrow \] b = 2 Hence, the values of a and b are 2 and 2, respectively.