# Answer to Question #42303 in Linear Algebra for anuirodh

Question #42303

a) Let a quadratic form have the expression x^2+y^2+2z^2+2xy+3xz with respect to the standard basis B1 ={(1,0,0),(0,1,0),(0,0,1)}.

Find its expression with respect to the basis B2 ={(1,1,1),(0,1,0),(0,1,1)}

b) Consider the quadratic form Q:2x^2âˆ’4xy+y^2+4xz+3z^2

i) Find a symmetric matrix A such that Q = XtAX.

ii) Find the orthogonal canonical reduction of the quadratic form.

iii) Find the principal axes of the form.

iv) Find the rank and signature of the form

Find its expression with respect to the basis B2 ={(1,1,1),(0,1,0),(0,1,1)}

b) Consider the quadratic form Q:2x^2âˆ’4xy+y^2+4xz+3z^2

i) Find a symmetric matrix A such that Q = XtAX.

ii) Find the orthogonal canonical reduction of the quadratic form.

iii) Find the principal axes of the form.

iv) Find the rank and signature of the form

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