Thank you.
i do not understand 4 or 5? 4. Given that Tis a linear transformation. Find the...
x 1.9.9 wuestion map Assume that Tis a linear transformation. Find the standard matrix of T. unchanged) and then reflects points through the line x2 + x4 T:R-R, first performs a horizontal shear that transforms e, into ez + 14, (leaving AO (Type an integer or simplified fraction for each matrix element.)
A Linear transformation T:R^5→R^4 is given as
How do I find the standard matrix of T, the zero space and
column-space of T?
How do I find the rank and the dimension of the zero-space of
T?
C1 x2 1 as C2 + 4- x5 C4 C5
5. (8 pts) Suppose B is a 4 x 5 matrix, and the associated linear transformation T(E) Bd, is onto. (a) (3) Find dim Nul(B) (b) (2) Does Ba 5 have a unique solution for every B (c) (3) Give a geometric interpretation to the solution set of Bt- 0
5. (8 pts) Suppose B is a 4 x 5 matrix, and the associated linear transformation T(E) Bd, is onto. (a) (3) Find dim Nul(B) (b) (2) Does Ba 5...
(12) (after 3.3) (a) Find a linear transformation T. Rº Rº such that T(x) = Ax that reflects a vector (1), 12) about the Tz-axis. (b) Find a linear transformation SR2 R2 such that T(x) = Bx that rotates a vector (2, 2) counterclockwise by 135 degrees. (c) Find a linear transformation (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). Give the matrix of this transformation explicitly. How...
[E] Consider the linear transformation T: R3 → R3 given by: T(X1, X2, X3) = (x1 + 2xz, 3x1 + x2 + 4x3, 5x1 + x2 + 8x3) (E.1) Write down the standard matrix for the transformation; i.e. [T]. (E.2) Obtain bases for the kernel of T and for the range of T. (E.3) Fill in the blanks below with the appropriate number. The rank of T = The nullity of T = (E.4) Is T invertible? Justify your response....
Please make sure the eigenspace is right.
5. Let T be the linear transformation given by T -2.22 + 4.23 -3x1 + x2 + 3.63 -X1 + x2 + 5x3] We know that the characteristic polynomial of T is -(t+2)(t – 4)2. (a) (8 pts) Find eigenvalues of T, and determine a basis for each eigenspace. (b) (8 pts) Let A denote the standard matrix of T, is A diagonalizable? Explain in full details.
15 points Save Ar 4) Find the standard matrix representing each given linear transformation. a) L: R3 R2 defined by L u2 4u U3 Find the standard matrix representing L. U1 0 b) L:R2 R3 defined by z ([,]) Find the standard matrix representing L. c) Find L(() using the standard matrix and linear transformation in part b. Do not type your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will...
b-c a (a) (5 points) Find a matrix representation for this linear transformation. (b) (3 points) What is the nullspace of this matrix? Write it as a span (e) (3 points) What is the column space of this matrix? Write it as a span.
(1 point) Let T be a linear transformation. Which of the following statements could be used to describe 77 (Select all that apply.) A. T(0) = 0 B. The columns of T are linearly independent. c. T is not empty. D. The domain of Tis R'. E. T contains (ie.. ). E T is a 3 x 4 matrix. G. T is one-to-one.
Consider the linear transformation TA, where A is given (4X5 matrix with one column (col 3) of zeroes. How do you determine whether it is a transformation R^4 to R^5 or R^5 to R^4 .