Question

Reduce the quadratic form
x
^2+4xy+6xz-y
^2+2yz+4z^2 to canonical form. Find rank, nature, index and signature of quadratic form.
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Answer 1

the index of the quadratic form is equal to the number of positive eight values of the matrix of quadratic form signature the index of the quadratic form is equal to the difference between the number of positive it values and number of negative eight values of the matrix of quadratic form