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Linear Algebra
Find the rank of the quadratic form 2x2+2y2+3z2-xy+4yz+5xz.
Linear Algebra
Let (V,<,>) be an inner product space over C and T belongs A(V). Prove that if <Tx , Ty>= <X,Y> for all X,Y belongs V, then T is unitary.
Linear Algebra
Let f: C3 to C be defined as f(Z)= (Z1-Z2)-i(2Z1+Z2+Z3). Where Z=(Z1,Z2,Z3) belongs to C3. Find aW belongs C3 such that f(Z)=<Z,W>, where <,> is the standard inner product on C3.
Linear Algebra
Find the equation of the plane passing through i-j , i+j and k.
Linear Algebra
show that the vectors V1=(i+2j-k)/2.236 , V2=(i+j)/1.414 , V3=(-i+j+k)/1.732 form an orhogonal basis for an orthogonal basis for R3. Further express X=i+j+2k as a linear combination of V1,V2 and V3.
Linear Algebra
Complete the set {(1,0,2) , (2,3,1) } to get a basis of R3.
Linear Algebra
FIND the basis of a subspace of R3 of the solution of the equation x+y+z=0.
Linear Algebra
If {V1,V2,V3} is a linearly independent set in R3 , then so is {V1+V2-2V3 , V1-2V2+V3 , -2V1+V2+V3}.
Linear Algebra
Every symmetric matrix with unit determinant is orthogonal.
Linear Algebra
If V is an eigenvector of an n*n invertible matrix A, then V is an eigennvector of the matrix A2. (T/F)
