Recent content by jwqwerty

  1. J

    On standardization of normal distribution

    Then what does standardization mean? How can we standardize? Sorry i have just started studying statistics and i need your help, statdad!
  2. J

    On standardization of normal distribution

    Let X be random variable and X~N(u,σ^2) Thus, normal distribution of x is f(x) = (1/σ*sqrt(2π))(e^(-(x-u)^2)/(2σ^2))) If we want to standardize x, we let z=(x-u)/σ Then the normal distribution of z becomes z(x) = (1/σ*sqrt(2π))(e^(-(x^2)/(2)) and we usually write Z~N(0,1) But as you can see...
  3. J

    How Do Eigenvectors Relate to Matrix Dimensions and Images?

    Homework Statement 1. If v is any nonzero vector in R^2, what is the dimension of the space V of all 2x2 matrices for which v is an eigenvector? 2. If v is an eigenvector of matrix A with associated eigenvalue 3, show that v is in the image of matrix A Homework Equations If v is an...
  4. J

    Proving CA⁻¹B+D=0 to Demonstrate Rank(A)=Rank([A B])=n

    you've got any idea on solving the problem?
  5. J

    Proving CA⁻¹B+D=0 to Demonstrate Rank(A)=Rank([A B])=n

    I want to show that det(D-CA‑¹B )=0 implies D-CA‑¹B=0 But i don't know how. Or are there any other ways?
  6. J

    Proving CA⁻¹B+D=0 to Demonstrate Rank(A)=Rank([A B])=n

    I have rewritten my question Fredrik!
  7. J

    Proving CA⁻¹B+D=0 to Demonstrate Rank(A)=Rank([A B])=n

    Ok i have rewritten my question since it looks very confusing
  8. J

    Proving CA⁻¹B+D=0 to Demonstrate Rank(A)=Rank([A B])=n

    if A B C D are nxn matrices such that rank(A)=rank([A B])=n ([A B] : 2nx2n matrix) [C D] [C D] we want to show that D=CA‑¹B (A‑¹: inverse matrix of A) this is what i have tried: [In 0] [A B] = [A B...
  9. J

    On derivatives of higher order

    if nth derivative of f at t (where t is in (a,b)) is defined, then this means that (n-1)th derivative of f is differentiable at t. since (n-1)th derivative of f is differentiable at t, (n-1)th derivative of f is continuous at t. In the same manner, we can argue that (n-2)th, (n-3)th... 1st...
  10. J

    On derivatives of higher order

    if g is differentiable on (a,b), it is continuous on (a,b) thus in the same manner we can say that (n-2)th derivative of f is continuous on (a,b) but what i want to know is whether (n-2) derivative of f is continuous on a and b
  11. J

    On derivatives of higher order

    let's assume that f(t) is a real function on [a,b], n is a positive integer (n-1)th derivative of f is continuous on [a,b], (n)th derivative exists for all t in (a,b) 1. Then can we say that (n-2)th derivative of f is continuous on [a,b]? 2. (n-2)th derivative of f is defined on a and b?
  12. J

    On limit of function and proof of chain rule

    In here, I must contain the range of f, thus f(x) cannot be 5. And also, s does not refer to specific number in I, like t in t->x
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