Question
If $\begin{bmatrix}\text{x}-\text{y}&\text{z}\\2\text{x}-\text{y}&\text{w}\end{bmatrix}=\begin{bmatrix}-1&4\\0&5\end{bmatrix},$ find x, y, z, w.
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Answer
Given, $\begin{bmatrix}\text{x}-\text{y}&\text{z}\\2\text{x}-\text{y}&\text{w}\end{bmatrix}=\begin{bmatrix}-1&4\\0&5\end{bmatrix}$ Since corresponding entries of equal matrices are equal, So x - y = -1 ...(i) z = 4 ...(ii) 2x - y = 0 ...(iii) w = 5 ...(iv) Solving equation (i) and (iii)
x = 1 Put x = 1 in equation (i), x - y = -1 1 - y = -1 -y = -1 - 1 -y = -2 y = 2 Equation (ii) and (iv) given the values of z and w respectively, So z = 4, w = 5 Hence, x = 1, y = 2, z = 4, w = 5
x = 1 Put x = 1 in equation (i), x - y = -1 1 - y = -1 -y = -1 - 1 -y = -2 y = 2 Equation (ii) and (iv) given the values of z and w respectively, So z = 4, w = 5 Hence, x = 1, y = 2, z = 4, w = 5
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