Linear Algebra

posted by .

(1) Define T:R->R be a linear transformation such that T(x,y,z)= (2x,2y,2z) then the given value of T is
A. 3
B. 2
C. 4
D. 6
(A) (B) (C) (D)

(2) Let V and W be vector spaces over a field F, and let T:V-> W be a linear transformation then only one of the following statement is correct
(A) V=R(T)
(B) Ker T/V=R(T)
(C)V/KerT=R(T)
(D) R(T)=DIM(T)

(A) (B) (C) (D)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Linear Algebra

    a)Let v be a fixed vector in R^3. Show that the transformation defined by T(u)=vxu is a linear transformation. b)Find the range of this linear transformation. Thanx
  2. Algebra

    Determine if the relationship represented in the table is linear. If it is linear, write an equation. x 2 5 7 10 12 20 y -3 0 2 5 7 15 A) Linear; y = x - -5 B) Linear; y = -5x C) Linear; y = x + -5 D) Not linear I'm thinking it's C …
  3. Linear Alebra

    Show that the transformation T:R^2->R^2 given T(x1,x2)=(3x1-5x2,x1+2x2) is linear by verifying that satisfies the definition of linear.
  4. Math

    Show that the transformation T:R^2->R^2 given T(x1,x2)=(3x1-5x2,x1+2x2) is linear by verifying that satisfies the definition of linear.
  5. Linear Algebra 2

    Let V and W be vector spaces over a field and let T:V->W be a linear transformation then V/kerT =R(T) (A) True (B) False (C) Indifference (D) None of the above (A) (B) (C) (D)
  6. Linear Algebra

    Consider the linear transformation T: R^3->R^3 which acts by rotation around the y-axis by an angle of pi, followed by a shear in the x-direction by a factor of 2. a) Find the matrix for T. Explain your method. b) What is T(1,2,3) …
  7. Linear Algebra

    2. Suppose that T is a linear transformation from R2 to R4 such that T ((1, 1)) = (3, −1, 4, −3) and T ((2, −1)) = (3, −2, −1, −3). Determine the matrix of T (with respect to the standard bases). …
  8. Linear Algebra

    Diagonalize the matrix A = [1,1;-2,4] using a similarity transformation. Give the transformation matrices such that (C^−1)AC = D, where D is a diagonal matrix. (D, C) = ?
  9. Linear Algebra

    Diagonalize the matrix A = [1,1;-2,4] using a similarity transformation. Give the transformation matrices such that (C^−1)AC = D, where D is a diagonal matrix. (D, C) = ?
  10. Linear Algebra

    Hello, could anyone help me with this excersise of linear algebra, Please?

More Similar Questions