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Which of the given values of x and y make the following pairs of matrices equal? [ 3 x + 7 5 y + 1 2 − 3 x ] , [ 0 y − 2 8 4 ]

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Question

Which of the given values of x and y make the following pairs of matrices equal? \[\begin{bmatrix}3x + 7 & 5 \\ y + 1 & 2 - 3x\end{bmatrix}, \begin{bmatrix}0 & y - 2 \\ 8 & 4\end{bmatrix}\] 

Options

  • x =\[- \frac{1}{3}\],y = 7 

  •  y = 7, x = \[- \frac{2}{3}\]  

  • x =  \[- \frac{1}{3}\] 4 =\[- \frac{2}{5}\]

  • Not possible to find

MCQ
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Solution

Not possible to find

\[Here, \] 

\[\begin{bmatrix}3x + 7 & 5 \\ y + 1 & 2 - 3x\end{bmatrix} = \begin{bmatrix}0 & y - 2 \\ 8 & 4\end{bmatrix}\] 

`"We know that for two equal matrices the corresponding elements are equal ."`

\[ \therefore 3x + 7 = 0, 5 = y - 2, y + 1 = \text{8 and 2 - 3x }= 4\] 

\[ \Rightarrow 3x = - 7, 5 + 2 = y, y =   \text{  8  -1   and - 3x}  = 4 - 2\] 

\[ \Rightarrow x = \frac{- 7}{3}, y = 7, y = \text{7 and x} = - \frac{2}{3} \] 

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Chapter 4: Algebra of Matrices - Exercise 5.7 [Page 68]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 4 Algebra of Matrices
Exercise 5.7 | Q 28 | Page 68

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