Find the value of x, if 3x+y&-y 2y-x&3 = 1&2 -5&3 - Vidyadip

Question

Find the value of x, if $\begin{bmatrix}3\text{x+y}&-\text{y}\\2\text{y}-\text{x}&3 \end{bmatrix}=\begin{bmatrix}1&2\\-5&3 \end{bmatrix}$

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Answer

The corresponding elements of two equal matrices are equal. Given: $\begin{bmatrix}3\text{x+y}&-\text{y}\\2\text{y}-\text{x}&3 \end{bmatrix}=\begin{bmatrix}1&2\\-5&3 \end{bmatrix}$ 3x + y = 1 ...(1) -y = 2 ⇒ y = -2Putting the value of y in eq. (1)
3x + (-2) = 1 ⇒ 3x -2 = 1 ⇒ 3x = 1 + 2 ⇒ 3x = 3 $\Rightarrow\text{x}=\frac{3}{3}=1$ $\therefore $ x = 1

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