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Physics Question on Mathematical Methods

The Jacobian matrix for transforming from (x, y) to another orthogonal coordinates system (u, v) as shown in the figure is
Graph x and y

A

12[11 1−1]\frac{1}{\sqrt2}\begin{bmatrix} 1 & 1 \\\ 1 & -1 \end{bmatrix}

B

12[11 −11]\frac{1}{\sqrt2}\begin{bmatrix} 1 & 1 \\\ -1 & 1 \end{bmatrix}

C

12[1−1 11]\frac{1}{\sqrt2}\begin{bmatrix} 1 & -1 \\\ 1 & 1 \end{bmatrix}

D

12[1−1 1−1]\frac{1}{\sqrt2}\begin{bmatrix} 1 & -1 \\\ 1 & -1 \end{bmatrix}

Answer

12[1−1 11]\frac{1}{\sqrt2}\begin{bmatrix} 1 & -1 \\\ 1 & 1 \end{bmatrix}

Explanation

Solution

The correct option is (C) : 12[1−1 11]\frac{1}{\sqrt2}\begin{bmatrix} 1 & -1 \\\ 1 & 1 \end{bmatrix}.