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Linear Algebra
Verify Cayley-Hamilton theorem of A= ( 1 2 2 3 1 0 1 1 1 )
Linear Algebra
Find the eigen value and eigen vector of A = [ 3 3 1 5 ]
Linear Algebra
If X=(-1,2,0), Y= (3,1,2), Z= (4,-1,0),show that linear combination at (0,1,-1).
Linear Algebra
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.
Linear Algebra
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
b. If T: R^5 to R^3 is a linear transformation, then there is u
Linear Algebra
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).
Linear Algebra
4x^2+3y^2+z^2-8xy-6yz+4zx
Linear Algebra
suppose s t ∈ l(v) are self-adjoint. Prove that st is self-adjoint if and only if st=ts
Linear Algebra
If X={D|D is a 2 x 2 diagonal matrix) and
D1~D2 iff D1 = c D2, c
D1~D2 iff D1 = c D2, c
Linear Algebra
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
< [X1], [Y1] > = X1^2+X2^2 define an inner
< [ X2], [Y2] >
Product over R^2.
True or false with full explanation
