- #1

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^{2}as g

_{ij}dx

^{i}dx

^{j}and

given dS

^{2}= (dx

^{1})

^{2}+ (dx

^{2})

^{2}+ 4(dx

^{1})(dx

^{2}). Find g

^{ij}

Now here is my take on the solution: Since the cross terms are present in the line element equation, we can say that it's a non-orthogonal system. So what I did was express the metric tensor in form of a 2x2 matrix, and checked the corresponding coefficient in the equation. But I am having a problem getting to the cross terms, and how to find the corresponding coefficients to the metric tensor.