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Find the orthogonal and Normal canonical reduction of the quadratic form 7x^2 +6xy+7y^2. Hence identify the conic represented by 7x^2+6xy+7y^2=200.. also find the principal axes of the given quadratic form.
a. Find a unit vector in R^3 that is orthogonal to (1,2,1) and (1,-1,2).
b. If T: R^5 to R^3 is a linear transformation, then there is u

Suppose n is a positive integer.Define T∈ L(Fn) by T(z1, z2,....., zn)=(0, z1,..., zn-1). Find a formula for T*(z1, z2,....., zn).


a. Find the orthogonal and normal canonical forms of 2y^2-2yz+2zx-2xy.

b. The operation,* defined by a*b= sin(ab), is a binary operation on N

True or false with full explanation



4x^2+3y^2+z^2-8xy-6yz+4zx


suppose s t ∈ l(v) are self-adjoint. Prove that st is self-adjoint if and only if st=ts


suppose t is a normal operator on v. suppose also that v, w €v satisfy the equations ||v||=||w||=2, tv =3v, tw =4w. show that ||t(v+w)||=10


If X={D|D is a 2 x 2 diagonal matrix) and

D1~D2 iff D1 = c D2, c
The function <,>: R^2×R^2 to R :
< [X1], [Y1] > = X1^2+X2^2 define an inner
< [ X2], [Y2] >
Product over R^2.
True or false with full explanation
a. Find a unit vector in R^3 that is orthogonal to (1,2,1) and (1,-1,2).
b. If T: R^5 to R^3 is a linear transformation, then there is u
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