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If \( \begin{bmatrix} 3a-b & -2b \\ 3 & 7 \end{bmatrix} = \begin{bmatrix} 5 & 3 \\ 3 & 7 \end{bmatrix}\) then find a.

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  • If the order of 2 matrices are equal, their corresponding elements are equal, i.e, if $A_{ij}=B_{ij}$, then any element $a_{ij}$ in matrix A is equal to corresponding element $b_{ij}$ in matrix B.
  • We can then match the corresponding elements and solve the resulting equations to find the values of the unknown variables.
$\begin{bmatrix} 3a-b & -2b \\ 3 & 7 \end{bmatrix} = \begin{bmatrix} 5 & 3 \\ 3 & 7 \end{bmatrix}$
The given two matrices are equal,hence their corresponding elements should be equal.
$\therefore\:3a-b=5$.....(i) and
$\Rightarrow\:b=\large \frac{-3}{2}$
Substitute the value of b in equation (i) we get
$\Rightarrow\:\large \frac{6a+3}{2}\normalsize =5$
$\Rightarrow\:a=\large \frac{7}{6}$
answered Apr 11, 2013 by sharmaaparna1
edited Mar 28, 2014 by rvidyagovindarajan_1

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