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  1. B

    Matrix and basis

    Consider a) f1=1, f2=sinx , f3=cosx b) f1=1, f2=ex , f3=e2x c)f1=e2x , f2=xe2x f3=x2e2x in each part B={f1,f2,f3} is a basis for a subspace V of the vector space. Find the matrix with respect to B of the differentiation operator D:V→V
  2. B

    Inner product of polynomials

    [-1]int[1]P(x)Q(x)dx P,Q\inS verify that this is an inner product.
  3. B

    Skew symmetric matrix

    what about thinking of rank-nullity theory since the dimension of this skew-symmetric matrix=n(n-1)/2 but how to calculate the dim of the AX=0
  4. B

    Skew symmetric matrix

    how can we prove that the rank of skew symmetric matrix is even i could prove it by induction is there another way
  5. B

    Denote standard inner product

    if A \in C nxn,show that (x,Ay)=0 for all x,y \in C[n], then A=0 (x,Ay) denote standard inner product on C[n]
  6. B

    Rank of matrix

    check that, for any nxn matrices A,B then rank(AB) (> or =) rank A +rank(B)-n
  7. B

    Show that if all the row sums of a matrix A belong to C (nxm) are

    show that if all the row sums of a matrix A belong to C (nxm) are zeroes, then A is singular. Hint. Observe that Ax=0 for x=[1 1 ....1]T
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