If x&3x-y 2x+z&3y-w = 3&2 4&7 , find x, y, z, w. - Vidyadip

Question

If $\begin{bmatrix}\text{x}&3\text{x}-\text{y}\\2\text{x}+\text{z}&3\text{y}-\text{w}\end{bmatrix}=\begin{bmatrix}3&2\\4&7\end{bmatrix},$ find x, y, z, w.

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Answer

Since all the corresponding elements of a matrix are equal,
$\begin{bmatrix}\text{x}&3\text{x}-\text{y}\\2\text{x}+\text{z}&3\text{y}-\text{w}\end{bmatrix}=\begin{bmatrix}3&2\\4&7\end{bmatrix}$
x = 3 ...(1)
3x - y = 2 ...(2)
Putting the value of x in eq. (2), we get
3(3) - y = 2
⇒ 9 - y = 2
⇒ -y = -7
⇒ y = 7
2x + z = 4 ...(3)
Putting the value of x in eq. (3), we get
2(3) + z = 4
⇒ 6 + z = 4
⇒ z = 4 - 6
⇒ z = -2
3y - w = 7 ...(4)
Putting the value of x in eq. (4), we get
3(7) - w = 7
⇒ 21 - w = 7
⇒ 21 - 7 = w
⇒ w = 14
$\therefore$ x = 3, y = 7, z = -2 and w = 14

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